A395432
Minimum k such that k^9 can be expressed as the sum of n distinct positive 9th powers.
DATA
917, 252, 202, 107, 66, 58, 69, 53, 47, 62, 59, 56, 58, 58, 55, 58, 49, 52, 56, 56, 58, 60, 59, 63, 63, 63, 66, 67, 66, 66, 69, 68, 71, 72, 69, 74, 75, 77, 76, 78, 79, 82, 81, 84, 82, 86, 84, 89, 88, 92, 93, 94, 94, 95, 97, 98, 98, 100
九次幂(A395432):
Total_time: 12.3276s
Total_states: 51475
Best_m: 107
Solution: 102 90 78 71 70 69 65 54 52 30 26 23 7
Total_time: 0.753595s
Total_states: 5495
Best_m: 66
Solution: 63 54 51 49 38 35 29 24 21 12 10 7 2 1
Total_time: 0.464574s
Total_states: 2904
Best_m: 58
Solution: 54 51 45 41 33 31 30 28 23 18 13 11 7 2 1
Total_time: 0.981999s
Total_states: 6469
Best_m: 69
Solution: 63 56 54 53 52 50 49 43 38 36 33 28 27 23 21 13
Total_time: 0.313828s
Total_states: 1842
Best_m: 53
Solution: 51 43 42 33 26 23 22 21 20 17 15 14 10 7 4 3 2
Total_time: 0.168418s
Total_states: 979
Best_m: 47
Solution: 43 39 38 36 33 32 31 30 27 26 18 15 14 11 7 4 2 1
Total_time: 0.66948s
Total_states: 3773
Best_m: 62
Solution: 58 55 44 42 39 38 35 29 27 23 22 21 19 18 15 13 11 2 1
Total_time: 0.530588s
Total_states: 2903
Best_m: 59
Solution: 57 47 44 38 37 35 34 33 32 31 30 28 21 19 17 15 8 6 4 3
Total_time: 0.41807s
Total_states: 2402
Best_m: 56
Solution: 50 48 46 43 41 38 36 34 29 28 25 21 20 19 17 16 15 14 12 9 5
Total_time: 0.498867s
Total_states: 2615
Best_m: 58
Solution: 52 51 49 42 38 33 31 30 28 26 23 22 21 20 18 17 16 15 12 9 8 7
Total_time: 0.516941s
Total_states: 2838
Best_m: 58
Solution: 54 47 46 42 41 39 38 37 36 34 32 31 28 26 25 19 14 12 9 8 7 2 1
Total_time: 0.366124s
Total_states: 2102
Best_m: 55
Solution: 49 46 44 42 41 40 39 37 32 31 30 28 26 25 19 18 16 14 13 11 9 8 5 2
Total_time: 0.459892s
Total_states: 2507
Best_m: 58
Solution: 50 48 46 45 44 43 42 41 40 37 36 34 30 28 23 22 20 17 12 10 9 5 3 2 1
Total_time: 0.168388s
Total_states: 1005
Best_m: 49
Solution: 43 42 41 37 36 33 32 31 30 29 27 26 24 22 20 19 18 16 13 11 10 9 7 6 5 2
Total_time: 0.228843s
Total_states: 1393
Best_m: 52
Solution: 48 43 41 38 37 35 34 33 32 31 30 29 27 26 25 23 22 19 17 16 10 9 8 7 5 4 3
Total_time: 0.356734s
Total_states: 2083
Best_m: 56
Solution: 50 49 44 42 39 38 37 36 35 34 32 30 27 22 21 18 16 15 14 13 12 11 6 5 4 3 2 1
Total_time: 0.338742s
Total_states: 1802
Best_m: 56
Solution: 52 47 44 42 38 37 34 33 32 30 29 28 27 22 20 19 18 17 16 14 12 10 9 8 6 5 4 2 1
Total_time: 0.387574s
Total_states: 2382
Best_m: 58
Solution: 54 52 40 37 36 35 34 32 31 30 29 26 25 24 23 19 18 17 16 14 13 12 11 8 7 5 4 3 2 1
Total_time: 0.488459s
Total_states: 2827
Best_m: 60
Solution: 53 49 48 47 44 43 42 41 40 39 37 35 33 32 31 30 27 25 24 21 20 18 15 14 10 7 5 4 3 2 1
Total_time: 0.425845s
Total_states: 2700
Best_m: 59
Solution: 52 50 48 46 44 41 39 38 37 35 34 30 29 28 27 26 25 24 22 20 17 16 14 13 12 11 10 8 5 4 3 1
Total_time: 0.64472s
Total_states: 3862
Best_m: 63
Solution: 58 50 49 48 47 45 44 40 39 36 34 33 32 31 30 27 26 24 22 18 16 14 13 12 11 9 8 7 6 5 4 3 2
Total_time: 0.601354s
Total_states: 3701
Best_m: 63
Solution: 57 51 50 47 46 45 44 43 41 40 38 37 36 34 28 27 26 24 22 21 20 19 17 16 15 14 12 11 7 5 4 3 2 1
Total_time: 0.542532s
Total_states: 3509
Best_m: 63
Solution: 56 54 51 47 46 44 42 40 39 38 36 34 32 31 30 28 27 26 25 24 22 21 20 19 18 17 16 15 14 13 12 9 8 5 4
Total_time: 0.682224s
Total_states: 3673
Best_m: 66
Solution: 59 58 50 49 47 46 43 42 41 39 38 37 36 35 32 31 30 29 28 27 26 25 24 22 21 18 16 15 14 12 10 9 6 5 4 2
Total_time: 0.75521s
Total_states: 4263
Best_m: 67
Solution: 57 56 53 52 51 49 48 46 45 44 43 42 40 38 37 35 34 33 32 30 29 28 26 25 24 23 20 18 17 15 13 12 11 10 7 3 1
Total_time: 0.549182s
Total_states: 3195
Best_m: 66
Solution: 57 56 53 52 51 48 46 43 39 38 37 36 35 32 31 30 29 28 26 24 23 22 21 20 19 18 17 16 15 13 12 11 9 6 5 4 3 1
Total_time: 0.490684s
Total_states: 3312
Best_m: 66
Solution: 55 54 53 52 51 50 48 47 44 43 42 39 38 37 36 35 34 33 32 30 29 28 26 25 24 23 22 19 18 16 15 14 13 12 11 10 9 7 2
Total_time: 0.672184s
Total_states: 3862
Best_m: 69
Solution: 63 58 56 51 48 45 44 43 41 40 39 38 37 36 34 33 32 31 29 28 27 26 25 23 22 21 20 17 16 15 14 13 12 11 9 8 7 4 2 1
Total_time: 0.539314s
Total_states: 3540
Best_m: 68
Solution: 58 56 54 53 52 50 49 48 45 44 43 42 41 40 38 37 34 33 30 29 26 25 24 22 21 20 19 18 17 14 11 10 9 8 7 6 5 4 3 2 1
Total_time: 0.859801s
Total_states: 4620
Best_m: 71
Solution: 62 58 57 56 55 53 48 47 46 43 42 39 38 37 36 35 34 33 32 31 30 29 27 26 24 23 22 21 20 19 17 16 15 13 12 11 10 8 7 4 3 2
Total_time: 0.864614s
Total_states: 4731
Best_m: 72
Solution: 63 58 57 56 55 53 50 49 47 46 45 44 43 42 41 40 39 38 37 35 34 33 32 31 27 25 24 22 21 18 17 16 15 14 12 11 10 9 7 6 5 3 2
Total_time: 0.424852s
Total_states: 3328
Best_m: 69
Solution: 57 56 55 54 53 51 50 49 48 47 46 44 43 41 40 39 38 37 36 35 33 32 31 30 29 28 27 25 24 23 22 20 19 16 15 14 13 9 8 7 6 4 3 2
Total_time: 0.907733s
Total_states: 4995
Best_m: 74
Solution: 65 62 58 57 55 53 51 50 49 47 46 45 43 42 40 39 38 37 35 34 32 29 28 27 25 24 23 22 21 18 17 16 15 14 12 11 10 9 8 7 6 5 4 3 2
Total_time: 1.08691s
Total_states: 5727
Best_m: 75
Solution: 65 64 58 57 56 54 53 51 50 49 47 46 44 42 40 39 37 36 35 34 33 31 30 29 28 27 25 24 23 21 20 18 17 16 15 14 13 12 10 8 7 6 5 3 2 1
Total_time: 1.88074s
Total_states: 6562
Best_m: 77
Solution: 67 63 61 59 58 56 54 53 52 51 50 47 45 44 43 42 41 40 39 38 37 36 35 34 32 30 29 28 27 26 25 23 22 21 19 18 17 16 15 13 12 9 8 5 4 2 1
Total_time: 0.760612s
Total_states: 5288
Best_m: 76
Solution: 64 61 60 59 57 56 55 54 53 52 51 49 48 47 46 44 42 41 40 39 38 37 36 35 34 31 30 27 26 25 24 22 21 20 18 17 16 15 14 13 12 11 9 8 7 5 4 3
Total_time: 1.10849s
Total_states: 5374
Best_m: 78
Solution: 67 65 61 59 58 57 55 54 53 52 51 50 49 48 45 44 43 42 40 38 35 33 32 31 30 29 27 26 25 24 23 22 21 20 17 16 15 14 13 12 11 10 8 7 6 4 3 2 1
Total_time: 1.12341s
Total_states: 5428
Best_m: 79
Solution: 69 65 62 60 59 57 56 54 53 52 51 49 47 46 45 44 43 42 41 40 39 38 37 36 34 32 31 30 28 27 26 25 24 22 21 20 19 18 16 14 13 11 10 8 7 6 5 4 2 1
Total_time: 3.26476s
Total_states: 6225
Best_m: 82
Solution: 76 63 62 60 59 58 57 56 54 52 51 50 47 46 44 43 42 41 40 39 38 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 16 14 13 10 7 6 5 4 3 2 1
Total_time: 1.10535s
Total_states: 5549
Best_m: 81
Solution: 70 66 63 62 61 58 57 56 55 54 53 52 51 50 48 47 46 45 44 43 42 41 40 39 38 37 35 34 33 32 30 29 27 25 22 21 20 19 18 17 15 11 10 9 8 7 6 5 4 3 2 1
Total_time: 3.08302s
Total_states: 7197
Best_m: 84
Solution: 73 67 65 64 63 62 60 59 58 57 56 55 52 50 49 48 46 45 44 42 41 40 38 37 36 35 34 33 32 31 29 28 27 26 25 24 22 21 20 18 17 16 14 11 10 9 8 7 6 5 4 3 2
Total_time: 0.6551s
Total_states: 4863
Best_m: 82
Solution: 70 67 65 64 62 60 58 57 55 54 53 52 51 50 49 45 44 43 42 41 39 38 37 36 35 33 31 30 29 28 27 26 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 3 2 1
Total_time: 3.31504s
Total_states: 7341
Best_m: 86
Solution: 72 69 68 67 66 62 61 60 59 58 57 56 55 54 53 52 51 49 48 47 46 45 43 41 40 39 38 37 36 35 34 32 31 30 29 27 25 24 23 21 20 18 17 16 15 14 12 11 10 9 8 7 6 2 1
Total_time: 0.569795s
Total_states: 4850
Best_m: 84
Solution: 70 69 65 64 63 62 61 60 58 57 56 55 54 53 52 50 49 48 47 46 44 42 40 38 37 36 35 34 33 32 31 29 28 27 26 25 24 23 22 21 20 19 18 17 16 14 13 12 11 9 8 7 5 4 3 2
Total_time: 5.55504s
Total_states: 8396
Best_m: 89
Solution: 77 73 71 68 67 65 62 61 59 58 56 55 54 53 52 51 49 48 47 46 44 43 42 41 40 39 38 36 34 33 32 31 29 28 25 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 3 2 1
Total_time: 1.39811s
Total_states: 6449
Best_m: 88
Solution: 71 70 69 68 67 66 65 64 62 61 60 58 56 55 54 53 52 51 50 48 47 46 45 44 43 42 41 40 39 37 36 35 34 33 32 31 30 29 27 26 25 24 23 21 19 17 16 14 12 10 9 8 7 6 4 3 2 1
Total_time: 13.0923s
Total_states: 8442
Best_m: 92
Solution: 80 73 71 70 68 66 65 64 63 62 61 60 59 58 57 56 54 53 52 50 49 48 47 46 45 44 43 42 41 40 38 37 36 35 34 33 31 30 28 27 26 24 23 22 21 20 18 17 15 14 13 12 10 9 8 6 4 3 1
Total_time: 16.5576s
Total_states: 9590
Best_m: 93
Solution: 78 76 75 71 69 67 66 65 64 63 62 60 59 58 56 55 54 53 51 49 48 47 46 45 44 42 41 39 38 37 36 35 34 31 30 29 28 27 26 25 24 23 22 21 20 19 16 15 14 13 12 9 8 7 6 5 4 3 2 1
Total_time: 11.4018s
Total_states: 8431
Best_m: 94
Solution: 80 79 72 71 70 68 67 66 64 62 61 60 59 58 56 55 54 53 51 50 49 48 47 46 45 43 42 41 39 38 37 34 33 32 31 30 28 27 26 25 24 23 21 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2
Total_time: 5.2786s
Total_states: 8394
Best_m: 94
Solution: 77 76 74 72 71 70 69 68 67 64 62 61 60 59 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 38 37 36 34 33 32 30 28 27 26 25 23 22 20 19 18 17 16 15 13 12 11 10 8 7 6 5 4 3 2 1
Total_time: 4.1068s
Total_states: 9557
Best_m: 95
Solution: 77 76 75 74 72 71 70 68 66 65 64 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 36 34 33 32 31 30 29 28 26 25 24 22 17 16 15 14 13 12 11 10 9 8 7 6 5 3 2 1
Total_time: 15.1464s
Total_states: 9511
Best_m: 97
Solution: 81 80 78 77 73 71 70 69 65 64 63 58 56 55 54 53 52 51 50 49 48 46 45 44 43 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Total_time: 5.68197s
Total_states: 9404
Best_m: 98
Solution: 84 78 76 74 73 72 71 70 68 65 64 63 62 61 60 59 58 57 56 55 54 53 52 50 47 46 45 44 42 41 40 39 38 37 36 35 34 33 32 30 29 28 27 25 24 23 22 21 20 19 18 16 15 14 12 11 10 9 8 7 6 4 3 2 1
Total_time: 2.70461s
Total_states: 9319
Best_m: 98
Solution: 79 78 77 76 75 73 71 70 68 67 66 65 64 63 61 60 59 58 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 21 20 19 17 16 15 14 12 11 10 8 6 3 2 1
Total_time: 4.23161s
Total_states: 9212
Best_m: 100
Solution: 87 78 76 75 74 73 72 70 69 68 67 66 65 64 63 60 59 58 57 56 55 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 35 34 33 31 30 29 27 26 25 24 23 22 20 19 18 17 16 15 14 12 11 9 8 7 6 5 4 3 2 1
Total_time: 29.5454s
Total_states: 11988
Best_m: 103
Solution: 84 82 80 78 77 76 75 74 73 72 71 70 68 67 65 64 63 62 61 59 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 38 37 36 35 34 33 32 31 30 28 27 26 25 23 22 21 20 19 16 15 14 13 12 11 10 9 8 7 5 4 3 2 1
Total_time: 22.6572s
Total_states: 10342
Best_m: 104
Solution: 84 81 80 79 78 77 76 75 74 73 72 70 69 68 67 66 65 64 62 61 60 59 57 55 54 53 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 21 20 19 18 17 14 13 12 8 7 6 4 2 1
Total_time: 45.492s
Total_states: 13382
Best_m: 106
Solution: 88 87 82 81 79 78 77 74 73 72 71 69 68 67 66 65 64 63 60 59 57 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 30 28 27 26 24 23 22 21 20 19 18 17 15 14 13 12 10 9 8 7 6 5 4 3 1
Total_time: 4.79056s
Total_states: 8594
Best_m: 105
Solution: 90 82 80 79 78 77 76 75 74 73 71 69 67 66 65 63 62 61 60 59 58 57 56 55 53 52 51 50 49 48 47 46 45 44 43 41 40 39 38 37 36 35 34 32 31 30 29 28 26 25 24 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 2
Total_time: 38.9562s
Total_states: 13065
Best_m: 108
Solution: 91 88 86 82 81 78 77 75 73 72 71 69 68 67 66 65 64 63 61 60 59 58 57 56 55 54 53 52 51 50 48 47 44 43 42 41 40 39 38 37 35 34 32 31 30 29 28 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 2 1
Total_time: 23.021s
Total_states: 11166
Best_m: 109
Solution: 86 85 84 83 82 81 80 79 78 77 76 75 74 73 71 69 67 64 63 62 61 60 59 58 57 56 55 54 53 52 51 48 47 46 45 44 42 41 40 39 38 37 36 35 34 33 32 30 29 28 27 25 24 23 22 21 20 19 18 17 15 14 13 12 10 9 8 7 6 4 3 2 1
Total_time: 8.64042s
Total_states: 10946
Best_m: 109
Solution: 90 85 84 83 82 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 62 61 60 59 58 57 56 55 54 53 52 51 50 48 47 46 45 44 43 42 41 40 36 35 34 33 32 30 29 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 7 6 4 3 2 1
Total_time: 42.7911s
Total_states: 14276
Best_m: 112
Solution: 90 87 86 85 84 83 81 80 79 78 77 76 75 74 72 71 70 69 68 67 66 65 64 63 62 61 59 58 57 55 54 53 52 51 50 49 48 47 45 43 42 41 40 39 37 35 34 33 32 31 30 28 27 26 25 24 22 21 18 17 16 15 14 13 12 11 9 8 7 6 5 4 3 2 1
Total_time: 96.7846s
Total_states: 14024
Best_m: 114
Solution: 98 88 86 85 84 83 82 81 79 78 77 76 75 74 73 72 71 70 68 65 64 63 62 60 59 58 57 55 54 53 52 50 49 47 46 45 44 42 41 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 16 15 14 13 12 11 10 9 8 7 6 4 3 2 1
Total_time: 93.1914s
Total_states: 15787
Best_m: 115
Solution: 98 90 87 86 85 84 83 82 80 79 78 77 76 74 73 72 69 68 67 66 65 63 62 61 60 59 58 57 56 55 54 53 52 51 49 48 47 46 43 42 41 40 39 38 37 36 35 34 33 31 30 29 28 27 26 25 24 23 22 21 19 18 17 16 15 14 12 11 10 9 8 7 5 4 3 2 1
Total_time: 19.3749s
Total_states: 11565
Best_m: 115
Solution: 95 93 88 87 86 84 82 81 80 78 77 76 75 74 73 72 71 70 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 48 47 46 45 42 41 40 39 38 36 35 34 33 31 30 29 28 27 26 25 24 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 4 3 2 1
Total_time: 135.322s
Total_states: 15178
Best_m: 118
Solution: 100 94 91 89 88 86 85 83 82 80 78 77 76 75 74 73 72 71 68 67 66 65 64 63 62 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 41 40 39 38 37 36 34 33 32 31 30 29 28 27 26 24 23 22 21 20 19 18 17 16 13 12 11 10 9 8 7 6 5 4 3 2 1
Total_time: 393.671s
Total_states: 19472
Best_m: 120
Solution: 100 95 92 91 88 87 86 85 84 83 81 80 79 78 77 76 75 73 72 71 70 68 67 66 64 62 61 60 59 57 56 55 54 53 52 51 50 47 46 45 44 43 42 41 40 39 38 37 36 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 16 15 14 13 12 11 9 8 7 6 5 4 3 2 1
Total_time: 107.343s
Total_states: 16706
Best_m: 120
Solution: 98 94 93 91 90 88 86 85 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 64 63 62 60 59 58 57 56 55 54 53 52 50 49 48 47 46 45 44 43 42 41 40 39 37 36 35 34 33 32 31 30 29 28 27 26 25 24 20 18 17 16 15 14 13 12 11 9 8 7 6 5 4 3 2
Total_time: 66.3158s
Total_states: 16312
Best_m: 121
Solution: 102 93 92 91 90 89 86 85 84 83 82 81 80 79 78 77 76 75 72 71 70 69 68 67 66 65 64 63 62 61 60 58 57 56 55 54 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 23 22 21 20 18 17 16 15 13 12 11 9 8 7 4 3 2 1
Total_time: 121.344s
Total_states: 18333
Best_m: 122
Solution: 98 97 96 95 90 88 87 86 85 83 82 81 80 79 78 77 76 75 74 73 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 50 49 48 47 46 45 44 43 42 41 40 39 37 36 35 34 33 32 31 30 29 27 26 25 24 23 21 20 19 18 15 14 13 12 11 10 9 8 6 4 3 2 1
Total_time: 421.011s
Total_states: 20514
Best_m: 125
Solution: 107 96 94 93 92 91 89 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 63 62 61 60 59 56 55 54 53 52 51 50 49 48 47 46 44 43 42 41 39 38 36 34 33 32 31 30 29 28 27 26 25 24 23 22 21 19 18 17 16 15 13 12 11 10 9 8 7 6 5 4 3 2 1
Total_time: 207.94s
Total_states: 17428
Best_m: 126
Solution: 98 97 96 95 94 93 92 90 89 88 87 86 85 84 83 82 81 80 79 78 76 75 74 73 72 71 69 68 67 66 65 63 62 61 60 59 58 57 56 55 54 52 51 50 46 45 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 21 20 18 16 15 13 12 11 10 9 8 7 6 5 4 3 2 1
Total_time: 203.049s
Total_states: 19570
Best_m: 127
Solution: 107 100 98 96 94 93 91 89 88 87 84 83 82 81 80 79 78 77 76 75 73 72 71 70 69 68 67 66 65 63 62 61 60 59 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 40 39 38 37 36 35 34 33 32 31 30 28 27 26 24 23 22 21 20 19 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Total_time: 38.7202s
Total_states: 14037
Best_m: 127
Solution: 113 100 93 92 91 90 89 88 86 85 84 82 81 80 79 78 77 76 75 74 73 72 71 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 43 42 41 40 39 38 37 36 35 34 33 31 29 28 27 26 25 24 23 21 20 19 18 17 16 15 14 13 12 11 10 8 7 6 5 4 3 2 1
Total_time: 840.519s
Total_states: 21329
Best_m: 131
Solution: 107 102 99 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 80 79 77 76 75 74 73 72 70 69 68 67 66 64 63 61 60 59 57 56 55 54 53 52 51 50 49 48 47 45 44 43 42 41 40 38 37 36 35 34 33 32 30 29 28 27 26 25 24 23 22 21 19 18 17 15 14 12 11 10 9 8 7 6 5 4 3 2 1
8次幂情况比较特殊，计算速度特别慢，其中n<=10时wolfram网站上有解。
n=11,
FOUND m=255
Solution: 246 196 186 170 126 122 112 106 92 33 6
n=12
FOUND m=149
142 122 110 92 74 72 64 53 42 34 28 2
n=13到21，分别m=119,119,109,113,103,85,95,89,91. (具体结果不小心覆盖了，需要后面重新处理）
n=22
Best_m: 99
Solution: 90 82 80 70 64 58 54 52 50 46 44 42 36 34 32 29 22 20 16 10 8 2
n=23
Best_m: 95
Solution: 82 78 76 74 66 65 64 58 52 48 44 42 40 38 36 26 24 22 20 16 8 6 2
n=24
FOUND m=99
Solution: 84 82 80 78 76 66 58 46 44 42 38 36 34 32 30 29 28 24 22 20 18 16 8 6
8次方的，n较大的场景
n=40
m=88
73 71 69 67 65 63 62 59 55 52 51 49 47 44 43 41 40 37 35 34 33 32 31 29 27 25 23 21 20 19 17 15 13 11 10 9 7 5 3 1
n=41
m=86
71 68 67 65 63 61 60 59 57 55 51 50 49 47 45 44 43 41 40 39 37 35 33 32 31 29 27 26 25 23 21 19 18 15 13 11 9 7 6 5 1
n=42
m=86
71 69 67 66 65 63 61 55 53 51 49 47 46 43 41 39 38 37 34 33 31 30 29 28 27 25 24 23 21 19 17 16 15 13 11 9 7 6 5 3 2 1
n=43
m=84
71 67 65 61 60 59 57 56 55 54 53 51 49 47 45 44 43 41 39 38 37 36 35 33 31 29 28 27 25 23 21 19 17 15 14 13 11 9 7 6 4 2 1
n=44
m=86
73 67 65 64 63 61 59 57 56 55 54 53 51 49 47 45 43 41 40 39 38 37 35 34 33 31 29 27 25 22 19 18 17 16 15 13 9 8 7 6 5 4 3 1
n=45
m=84
69 68 65 63 61 59 58 56 55 54 53 51 49 47 45 43 40 39 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 21 19 17 15 13 11 9 7 5 4 3 1
n=46
m=84
73 67 65 63 59 57 56 55 53 51 50 49 47 45 43 42 39 37 35 34 33 32 31 30 29 27 26 25 24 23 22 21 20 19 17 16 15 12 11 9 8 7 6 5 3 1
n=47
m=84
73 69 63 61 59 58 57 53 52 51 49 48 47 46 45 43 42 41 39 38 37 35 33 32 29 27 26 25 24 23 21 19 18 17 16 15 14 13 12 11 10 9 7 5 3 2 1
n=48
m=86
69 67 65 64 63 61 60 59 58 57 55 54 53 52 51 49 48 47 45 44 42 41 40 39 37 36 35 34 33 32 31 29 27 26 23 21 19 17 13 11 9 8 7 6 5 3 2 1
n=49
m=86
73 71 67 65 63 61 59 53 51 47 46 45 43 42 41 40 39 38 37 36 35 33 32 31 30 29 28 27 26 25 22 21 19 17 16 15 14 13 12 11 9 8 7 6 5 4 3 2 1
n=50
m=86
73 71 67 64 63 61 57 53 51 50 49 48 47 45 43 42 41 39 38 37 35 34 33 32 31 30 29 27 26 25 23 22 21 20 19 18 17 15 14 13 12 11 10 9 8 7 6 5 2 1
n=51
m=86
71 70 67 66 63 61 57 55 54 53 51 50 49 48 47 45 43 41 40 39 38 37 36 33 32 31 29 28 27 26 25 23 22 21 20 19 18 17 16 15 13 11 10 9 7 6 5 4 3 2 1
n=52
m=86
71 69 64 63 62 61 60 59 57 55 54 53 52 51 49 47 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 28 27 26 25 24 23 21 20 19 17 15 14 11 10 9 7 5 4 3 1
n=53
m=86
70 68 67 65 61 60 59 57 56 55 54 53 52 51 50 49 48 47 45 44 43 42 41 39 37 35 34 33 31 30 29 27 26 24 23 22 21 20 19 17 16 15 14 13 11 10 9 8 7 5 3 2 1
n=54
m=88
71 69 67 66 64 63 61 59 58 57 56 55 54 53 51 50 49 48 46 45 44 43 41 40 39 38 37 36 35 34 33 32 31 29 27 25 24 23 21 19 18 17 15 14 12 11 9 8 6 5 4 3 2 1
n=55
m=88
73 69 66 65 64 63 61 59 58 57 56 55 53 52 51 50 48 47 44 43 41 40 39 37 36 33 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 11 9 8 7 6 5 4 3 2 1
n=56
m=89
74 67 66 65 64 63 62 61 60 59 57 56 55 54 53 52 51 49 48 47 46 45 43 42 41 39 38 37 35 34 33 30 29 28 27 26 25 23 22 21 20 19 17 15 13 12 11 9 8 7 6 5 4 3 2 1
n=57
m=90
72 70 69 68 67 65 62 61 59 58 57 56 55 54 53 52 49 47 45 44 43 42 41 40 39 38 37 35 34 33 31 30 29 27 26 25 24 23 22 21 20 19 18 16 15 14 13 12 11 10 9 8 7 6 5 3 1
n=58
m=91
75 72 68 67 65 63 62 61 60 59 58 57 56 55 54 53 52 51 49 48 47 46 45 43 42 40 39 38 37 36 35 31 29 27 26 25 24 23 21 20 19 18 17 16 15 13 12 11 10 9 8 7 6 5 4 3 2 1
n=59
m=92
75 71 70 69 68 66 65 61 60 59 58 57 56 55 53 51 50 49 48 47 46 45 44 43 41 40 39 38 37 36 34 33 32 31 30 29 28 27 25 22 21 19 18 17 16 15 14 13 12 11 10 8 7 6 5 4 3 2 1
n=60
m=90
72 71 67 66 65 64 63 61 60 59 58 57 56 55 54 52 51 50 49 48 47 46 45 44 42 41 40 39 38 37 36 35 34 33 32 31 29 28 27 24 23 22 21 20 19 18 17 16 15 13 11 9 8 7 6 5 4 3 2 1
n=61
m=94
79 73 72 69 68 66 65 64 63 59 58 57 55 54 52 51 50 49 48 47 46 45 44 43 42 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 19 18 17 16 14 13 11 10 9 8 7 6 5 4 3 1
n=62
m=94
77 71 70 69 68 67 66 64 63 62 61 59 58 57 56 55 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 16 15 14 12 11 8 7 6 5 4 1
n=63
m=95
76 75 72 70 69 67 65 64 63 62 61 60 59 58 57 55 54 53 52 51 49 48 46 45 44 43 42 41 40 39 38 37 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 15 14 13 12 11 9 8 7 6 5 4 3 2
n=64
m=96
78 75 73 71 70 67 66 65 63 62 61 60 59 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 38 37 36 35 34 33 32 31 28 27 26 25 24 23 22 21 20 18 17 16 15 14 13 12 11 10 9 8 6 4 3 2 1
n=65
m=98
80 74 72 71 70 69 68 67 66 65 64 63 62 61 60 59 57 56 55 54 53 52 50 49 47 46 45 44 43 42 40 39 38 37 36 35 32 29 28 27 26 25 24 23 22 21 20 19 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
n=66
m=101
78 77 76 74 73 72 71 69 68 67 66 65 64 63 62 61 60 59 58 56 55 54 53 52 50 49 48 47 46 45 44 43 42 41 39 38 37 36 35 34 33 32 31 29 27 26 25 23 22 21 20 18 17 16 14 13 12 10 9 7 6 5 4 3 2 1
n=67
m=100
79 76 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 56 52 51 50 49 48 47 46 45 44 43 40 39 38 36 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
n=68
m=101
81 78 77 74 73 72 71 70 67 66 64 63 62 61 59 58 57 56 55 54 53 52 51 50 49 48 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 10 9 8 7 6 5 4 2
n=69
m=103
83 78 76 75 74 73 72 71 70 69 68 66 64 63 62 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 17 16 14 13 12 11 10 9 5 4 3 2 1
n=70
m=105
83 82 80 79 78 74 72 70 69 68 67 66 65 64 62 60 59 58 57 56 55 54 53 52 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 21 20 19 18 17 16 15 14 13 12 11 10 7 6 5 4 3 1
n=71
m=107
84 81 80 78 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 57 56 55 54 53 52 51 50 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 32 31 30 29 28 27 25 24 22 21 20 19 18 17 16 14 11 10 9 8 6 5 4 3 2 1
n=72
m=111
88 87 84 83 82 79 78 76 74 72 69 68 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 27 26 24 23 22 21 20 19 18 16 15 14 13 12 11 9 8 7 6 5 4 3 2 1
n=73
m=111
88 85 84 82 81 80 77 75 74 72 71 70 69 68 67 66 65 64 62 61 60 58 56 55 54 53 50 49 48 47 46 45 44 43 42 41 40 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 12 11 10 9 8 7 6 5 4 2 1
n=74
m=114
92 88 86 84 82 80 77 76 75 74 73 72 71 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 42 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 24 21 20 19 18 16 15 14 12 11 10 9 8 7 6 4 3 2 1
周末有个比较大的突破，由于任何一个偶数的8次方模32为0，奇数的8次方模32为1，那么任何时候，余下h个8次方和如果要求对应的和的余下模32大于h,必然无解，使用了这个方案以后，对于比较小的n非常有效，大大提升了计算效率。
而在这之前，分别试验了模5,模17，两者对于8次方幂的情况应该都有一些作用，但是效果不明显；而模32的效果特别明显，速度至少是几十倍的提升。
另外也顺便验算了n=10的情况，wolfram上的结果的确是已知最小的结果
A394259
n=11
m=255
246 196 186 170 126 122 112 106 92 33 6
n=12
m=149
142 122 110 92 74 72 64 53 42 34 28 2
n=13
m=119
106 102 96 84 80 74 64 40 32 23 14 4 2
n=14
m=119
108 100 94 86 84 58 40 36 28 23 20 16 6 2
n=15
m=109
100 94 86 70 58 54 46 45 44 42 26 24 10 6 4
n=16
m=113
108 86 84 79 74 56 52 48 38 36 34 28 26 12 8 6
n=17
m=103
98 76 74 72 71 66 64 54 48 46 42 40 32 28 24 18 16
n=18
m=85
78 70 68 58 54 53 50 42 38 36 34 30 24 22 14 12 6 2
n=19
m=95
82 80 76 70 66 65 62 58 56 52 48 44 38 30 26 24 18 6 2
n=20
m=89
78 74 72 70 60 58 52 42 38 36 34 28 22 20 18 16 10 7 6 4
n=21
m=91
82 80 64 62 60 58 56 50 46 44 40 38 36 32 24 18 16 6 5 4 2
n=22
m=99
96 70 66 64 62 60 58 56 54 52 50 42 40 34 30 29 28 22 20 18 14 8
n=23
m=95
82 78 76 74 66 65 64 58 52 48 44 42 40 38 36 26 24 22 20 16 8 6 2
n=24
m=99
84 82 80 78 76 66 58 46 44 42 38 36 34 32 30 29 28 24 22 20 18 16 8 6
n=25
m=93
80 76 72 70 68 66 64 60 56 54 48 46 44 38 34 32 29 28 26 24 18 14 10 8 4
n=26
m=103
89 86 80 76 74 72 70 66 60 56 52 48 46 44 40 34 32 26 24 22 20 16 12 6 4 2
n=27
m=99
90 78 76 74 70 68 60 58 54 52 48 46 44 42 40 36 34 30 29 28 26 24 20 16 8 4 2
n=28
m=103
90 84 80 78 76 70 66 64 62 60 50 48 46 42 40 39 38 36 34 32 24 22 16 12 10 8 6 2
n=29
m=105
98 82 80 74 68 66 64 60 56 55 54 52 48 46 44 38 36 34 32 28 26 22 20 18 16 14 12 6 4
n=30
m=103
88 86 82 78 72 70 66 64 62 60 58 54 52 48 46 44 40 39 38 36 34 32 26 24 20 18 16 8 6 4
n=31
m=115
96 92 90 88 86 84 80 76 72 68 64 62 60 58 52 48 42 40 38 34 32 30 28 22 20 14 13 8 6 4 2
n=32
m=109
102 82 78 76 74 72 70 68 66 62 58 56 54 52 50 48 44 40 38 36 34 30 26 22 20 19 18 16 14 10 6 2
n=33
m=110
95 91 87 81 79 77 73 67 63 61 59 57 55 53 51 50 47 45 43 41 39 35 31 29 27 25 17 15 13 9 5 3 1
n=34
m=104
91 83 81 79 75 73 69 65 63 59 57 55 53 49 45 41 39 35 33 31 25 24 23 21 19 17 15 13 11 9 7 5 4 1
n=35
m=100
87 83 77 74 71 67 65 63 61 59 57 55 53 51 49 43 41 39 38 37 35 31 29 27 25 23 21 19 18 17 11 9 5 3 1
n=36
m=98
87 78 77 73 71 63 61 60 59 57 55 53 51 49 47 45 43 41 39 37 35 34 33 31 29 27 23 21 17 15 13 11 9 8 3 1
n=37
m=88
73 71 69 67 65 63 61 59 56 55 53 49 47 39 37 36 35 34 33 31 29 27 25 24 23 21 19 17 15 13 12 11 9 7 5 3 1
n=38
m=94
79 73 72 71 70 69 67 63 59 57 55 53 52 51 49 48 47 46 45 43 41 39 37 35 33 31 29 27 25 23 19 18 15 13 7 5 3 1
n=39
m=90
79 73 69 67 65 63 61 55 53 51 49 46 45 43 41 40 39 36 35 33 31 30 29 27 26 25 23 22 19 17 15 13 11 9 7 5 3 2 1
n=40
m=88
73 71 69 67 65 63 62 59 55 52 51 49 47 44 43 41 40 37 35 34 33 32 31 29 27 25 23 21 20 19 17 15 13 11 10 9 7 5 3 1
n=41
m=86
71 68 67 65 63 61 60 59 57 55 51 50 49 47 45 44 43 41 40 39 37 35 33 32 31 29 27 26 25 23 21 19 18 15 13 11 9 7 6 5 1
n=42
m=86
71 69 67 66 65 63 61 55 53 51 49 47 46 43 41 39 38 37 34 33 31 30 29 28 27 25 24 23 21 19 17 16 15 13 11 9 7 6 5 3 2 1
n=43
m=84
71 67 65 61 60 59 57 56 55 54 53 51 49 47 45 44 43 41 39 38 37 36 35 33 31 29 28 27 25 23 21 19 17 15 14 13 11 9 7 6 4 2 1
n=44
m=86
73 67 65 64 63 61 59 57 56 55 54 53 51 49 47 45 43 41 40 39 38 37 35 34 33 31 29 27 25 22 19 18 17 16 15 13 9 8 7 6 5 4 3 1
n=45
m=84
69 68 65 63 61 59 58 56 55 54 53 51 49 47 45 43 40 39 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 21 19 17 15 13 11 9 7 5 4 3 1
n=46
m=84
73 67 65 63 59 57 56 55 53 51 50 49 47 45 43 42 39 37 35 34 33 32 31 30 29 27 26 25 24 23 22 21 20 19 17 16 15 12 11 9 8 7 6 5 3 1
n=47
m=84
73 69 63 61 59 58 57 53 52 51 49 48 47 46 45 43 42 41 39 38 37 35 33 32 29 27 26 25 24 23 21 19 18 17 16 15 14 13 12 11 10 9 7 5 3 2 1
n=48
m=86
69 67 65 64 63 61 60 59 58 57 55 54 53 52 51 49 48 47 45 44 42 41 40 39 37 36 35 34 33 32 31 29 27 26 23 21 19 17 13 11 9 8 7 6 5 3 2 1
n=49
m=86
73 71 67 65 63 61 59 53 51 47 46 45 43 42 41 40 39 38 37 36 35 33 32 31 30 29 28 27 26 25 22 21 19 17 16 15 14 13 12 11 9 8 7 6 5 4 3 2 1
n=50
m=86
73 71 67 64 63 61 57 53 51 50 49 48 47 45 43 42 41 39 38 37 35 34 33 32 31 30 29 27 26 25 23 22 21 20 19 18 17 15 14 13 12 11 10 9 8 7 6 5 2 1
n=51
m=86
71 70 67 66 63 61 57 55 54 53 51 50 49 48 47 45 43 41 40 39 38 37 36 33 32 31 29 28 27 26 25 23 22 21 20 19 18 17 16 15 13 11 10 9 7 6 5 4 3 2 1
n=52
m=86
71 69 64 63 62 61 60 59 57 55 54 53 52 51 49 47 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 28 27 26 25 24 23 21 20 19 17 15 14 11 10 9 7 5 4 3 1
n=53
m=86
70 68 67 65 61 60 59 57 56 55 54 53 52 51 50 49 48 47 45 44 43 42 41 39 37 35 34 33 31 30 29 27 26 24 23 22 21 20 19 17 16 15 14 13 11 10 9 8 7 5 3 2 1
n=54
m=88
71 69 67 66 64 63 61 59 58 57 56 55 54 53 51 50 49 48 46 45 44 43 41 40 39 38 37 36 35 34 33 32 31 29 27 25 24 23 21 19 18 17 15 14 12 11 9 8 6 5 4 3 2 1
n=55
m=88
73 69 66 65 64 63 61 59 58 57 56 55 53 52 51 50 48 47 44 43 41 40 39 37 36 33 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 11 9 8 7 6 5 4 3 2 1
n=56
m=89
74 67 66 65 64 63 62 61 60 59 57 56 55 54 53 52 51 49 48 47 46 45 43 42 41 39 38 37 35 34 33 30 29 28 27 26 25 23 22 21 20 19 17 15 13 12 11 9 8 7 6 5 4 3 2 1
n=57
m=90
72 70 69 68 67 65 62 61 59 58 57 56 55 54 53 52 49 47 45 44 43 42 41 40 39 38 37 35 34 33 31 30 29 27 26 25 24 23 22 21 20 19 18 16 15 14 13 12 11 10 9 8 7 6 5 3 1
n=58
m=91
75 72 68 67 65 63 62 61 60 59 58 57 56 55 54 53 52 51 49 48 47 46 45 43 42 40 39 38 37 36 35 31 29 27 26 25 24 23 21 20 19 18 17 16 15 13 12 11 10 9 8 7 6 5 4 3 2 1
n=59
m=92
75 71 70 69 68 66 65 61 60 59 58 57 56 55 53 51 50 49 48 47 46 45 44 43 41 40 39 38 37 36 34 33 32 31 30 29 28 27 25 22 21 19 18 17 16 15 14 13 12 11 10 8 7 6 5 4 3 2 1
n=60
m=90
72 71 67 66 65 64 63 61 60 59 58 57 56 55 54 52 51 50 49 48 47 46 45 44 42 41 40 39 38 37 36 35 34 33 32 31 29 28 27 24 23 22 21 20 19 18 17 16 15 13 11 9 8 7 6 5 4 3 2 1
n=61
m=94
79 73 72 69 68 66 65 64 63 59 58 57 55 54 52 51 50 49 48 47 46 45 44 43 42 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 19 18 17 16 14 13 11 10 9 8 7 6 5 4 3 1
n=62
m=94
77 71 70 69 68 67 66 64 63 62 61 59 58 57 56 55 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 16 15 14 12 11 8 7 6 5 4 1
n=63
m=95
76 75 72 70 69 67 65 64 63 62 61 60 59 58 57 55 54 53 52 51 49 48 46 45 44 43 42 41 40 39 38 37 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 15 14 13 12 11 9 8 7 6 5 4 3 2
n=64
m=96
78 75 73 71 70 67 66 65 63 62 61 60 59 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 38 37 36 35 34 33 32 31 28 27 26 25 24 23 22 21 20 18 17 16 15 14 13 12 11 10 9 8 6 4 3 2 1
n=65
m=98
80 74 72 71 70 69 68 67 66 65 64 63 62 61 60 59 57 56 55 54 53 52 50 49 47 46 45 44 43 42 40 39 38 37 36 35 32 29 28 27 26 25 24 23 22 21 20 19 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
n=66
m=101
78 77 76 74 73 72 71 69 68 67 66 65 64 63 62 61 60 59 58 56 55 54 53 52 50 49 48 47 46 45 44 43 42 41 39 38 37 36 35 34 33 32 31 29 27 26 25 23 22 21 20 18 17 16 14 13 12 10 9 7 6 5 4 3 2 1
n=67
m=100
79 76 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 56 52 51 50 49 48 47 46 45 44 43 40 39 38 36 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
n=68
m=101
81 78 77 74 73 72 71 70 67 66 64 63 62 61 59 58 57 56 55 54 53 52 51 50 49 48 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 10 9 8 7 6 5 4 2
n=69
m=103
83 78 76 75 74 73 72 71 70 69 68 66 64 63 62 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 17 16 14 13 12 11 10 9 5 4 3 2 1
n=70
m=105
83 82 80 79 78 74 72 70 69 68 67 66 65 64 62 60 59 58 57 56 55 54 53 52 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 21 20 19 18 17 16 15 14 13 12 11 10 7 6 5 4 3 1
n=71
m=107
84 81 80 78 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 57 56 55 54 53 52 51 50 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 32 31 30 29 28 27 25 24 22 21 20 19 18 17 16 14 11 10 9 8 6 5 4 3 2 1
n=72
m=111
88 87 84 83 82 79 78 76 74 72 69 68 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 27 26 24 23 22 21 20 19 18 16 15 14 13 12 11 9 8 7 6 5 4 3 2 1
n=73
m=111
88 85 84 82 81 80 77 75 74 72 71 70 69 68 67 66 65 64 62 61 60 58 56 55 54 53 50 49 48 47 46 45 44 43 42 41 40 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 12 11 10 9 8 7 6 5 4 2 1
n=74
m=114
92 88 86 84 82 80 77 76 75 74 73 72 71 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 42 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 24 21 20 19 18 16 15 14 12 11 10 9 8 7 6 4 3 2 1
n=75
m=115
94 90 84 83 82 80 79 78 77 76 74 72 71 70 69 68 67 66 65 64 63 62 59 58 56 55 54 52 51 50 49 48 47 46 45 44 43 41 40 39 38 37 36 35 34 33 32 31 30 28 27 26 25 24 22 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
n=76
m=118
94 91 88 86 85 84 82 80 78 77 76 75 74 73 72 71 68 67 66 65 64 63 62 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 40 39 38 37 36 34 32 30 29 28 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 10 9 8 6 5 4 3 2 1
n=77
m=120
94 92 90 88 86 84 83 82 81 79 78 77 76 75 74 73 72 70 68 67 66 64 63 62 60 59 58 57 56 54 52 51 50 49 48 47 46 44 43 42 41 40 38 37 36 35 34 33 31 30 29 28 27 26 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 6 5 4 3 2 1
n=78
m=121
94 92 90 88 87 86 84 83 82 81 80 78 77 76 75 72 71 70 69 68 67 66 65 64 63 62 60 58 56 55 54 50 49 48 47 46 45 44 42 41 40 39 38 37 36 35 34 32 31 30 29 28 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
n=79
m=125
100 99 94 92 91 88 85 84 82 80 78 77 76 75 74 73 72 71 70 69 68 67 66 64 62 61 60 59 58 57 56 55 54 52 51 50 49 48 47 46 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 26 25 24 23 22 21 20 19 18 16 14 12 11 10 9 8 7 6 4 3 2 1
n=80
m=125
100 96 93 92 90 88 86 84 82 81 80 79 78 77 76 74 73 72 71 70 69 68 67 66 65 64 63 61 60 59 58 56 55 54 53 52 51 50 48 47 46 45 44 43 42 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 24 23 22 21 20 18 16 14 13 12 10 9 8 7 6 5 4 3 2 1
n=81
m=129
102 96 94 93 92 91 90 89 88 86 85 84 82 80 79 78 77 76 74 73 72 71 70 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 52 51 50 49 48 47 46 43 42 41 40 38 37 36 35 34 33 32 31 30 28 27 26 25 24 23 22 20 19 18 17 16 15 14 13 12 11 10 8 7 6 4 2
下面这个是搜索代码，需要在Linux上面使用，适合多核机器进行多进程搜索
#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <unistd.h>
#include <sys/wait.h>
#include <signal.h>
#include <cstring>
#include <dirent.h>
#include <fstream>
#include <sstream>
#include <queue>
#include <map>
#include <sys/stat.h>
using namespace std;
typedef __int128_t ll;
int n, k;
vector<ll> T;
unsigned long T_max = 0;
struct State { ll remaining, x3, x2, x1; };
ll mymax(ll a, ll b) { return a >= b ? a : b; }
ll power(ll x) {
ll r = 1;
for (int i = 0; i < k; i++) r *= x;
return r;
}
ostream& operator<<(ostream& os, __int128_t n) {
if (n < 0) { os << '-'; n = -n; }
if (n == 0) return os << '0';
char buf; int i = 0;
while (n > 0) { buf = '0' + (n % 10); n /= 10; }
while (i--) os << buf;
return os;
}
istream& operator>>(istream& is, __int128_t& n) {
string s; is >> s; n = 0;
bool neg = false; size_t start = 0;
if (s == '-') { neg = true; start = 1; }
for (size_t i = start; i < s.size(); i++) n = n * 10 + (s - '0');
if (neg) n = -n;
return is;
}
void ensureT(unsigned long maxVal) {
if (maxVal <= T_max) return;
T.resize(maxVal + 1);
ll sum = (T_max > 0) ? T : 0;
for (unsigned long i = T_max + 1; i <= maxVal; i++) { sum += power((ll)i); T = sum; }
T_max = maxVal;
}
void initT(unsigned long maxVal) {
T.resize(maxVal + 1); T = 0; ll sum = 0;
for (unsigned long i = 1; i <= maxVal; i++) { sum += power((ll)i); T = sum; }
T_max = maxVal;
}
bool canAchieveMod7(ll X, int h, int r) {
ll max7multiples = (X - 1) / 7;
ll maxK = mymax(min((ll)(h - 1), max7multiples), (ll)0);
ll minK = mymax(max7multiples - (X - h), (ll)0);
if (minK > maxK) return false;
ll lb = (h - 1 - maxK) % 7; if (lb < 0) lb += 7;
ll hb = (h - 1 - minK) % 7; if (hb < 0) hb += 7;
if (hb >= lb) return r <= hb && r >= lb;
else return r <= hb || r >= lb;
}
bool canAchieveMod5(ll X, int h, int r) {
ll max5multiples = (X - 1) / 5;
ll maxK = mymax(min((ll)(h - 1), max5multiples), (ll)0);
ll minK = mymax(max5multiples - (X - h), (ll)0);
if (minK > maxK) return false;
ll lb = (h - 1 - maxK) % 5; if (lb < 0) lb += 5;
ll hb = (h - 1 - minK) % 5; if (hb < 0) hb += 5;
if (hb >= lb) return r <= hb && r >= lb;
else return r <= hb || r >= lb;
}
bool canAchieveMod32(ll X, int h, int r){
if(h-1<r)return false;
return true;
}
int pow8mod17;
int U;
bool mod17_initialized = false;
void initMod17() {
if (mod17_initialized) return;
for (int i = 1; i <= 16; i++) {
ll p = 1;
for (int j = 0; j < 8; j++) p *= i;
pow8mod17 = (int)(p % 17);
}
U = 0;
for (int i = 1; i <= 16; i++) {
U = U + (pow8mod17 == 1 ? 1 : 0);
}
mod17_initialized = true;
}
bool canAchieveMod17(ll X, int h, ll rem) {
int u = (int)(rem % 17);
if (u < 0) u += 17;
ll X1 = X - 1;
ll fullCycles = X1 / 17;
int remainder = (int)(X1 % 17);
ll count0 = fullCycles;
ll count1 = fullCycles * 8 + U;
ll countNeg1 = fullCycles * 8 + remainder - U;
ll min1neg1 = min(count1, countNeg1);
if (u == 0) {
if((h&1)&&count0==0)return false;
ll minPairs = (h - count0 + 1) / 2;
if (minPairs < 0) minPairs = 0;
return min1neg1 >= minPairs;
}
auto tryCase = [&](ll need1, ll needNeg1, ll need0) -> bool {
if (need1 > count1) return false;
if (needNeg1 > countNeg1) return false;
if (need0 > count0) return false;
ll remaining = h - need1 - needNeg1 - need0;
if (remaining < 0) return false;
ll avail1 = count1 - need1;
ll availNeg1 = countNeg1 - needNeg1;
ll avail0 = count0 - need0;
ll minAvail = min(avail1, availNeg1);
ll maxByPairs = 2 * minAvail;
if (remaining > maxByPairs + avail0) return false;
if (remaining % 2 == 1 && avail0 == 0) return false;
return true;
};
if (count1 >= u) {
if (tryCase(u, 0, 0)) return true;
}
if (countNeg1 >= (17 - u)) {
if (tryCase(0, 17 - u, 0)) return true;
}
return false;
}
void collect_stat(ll rem, int h, ll prevX, vector<ll>& xs, vector<State>& states, int n) {
if (h == n - 3) { State s; s.remaining = rem; s.x3 = xs; s.x2 = xs; s.x1 = xs; states.push_back(s); return; }
if (rem < T) return;
ll upper = rem - T; if (upper <= 0) return;
ll maxX = (ll)(pow((double)upper, 1.0 / k)) + 1;
while (maxX > 0 && (unsigned long)maxX < T.size() && power(maxX) > upper) maxX--;
if (maxX >= prevX) maxX = prevX - 1;
ll minX = h; if (minX > maxX) return;
for (ll x = maxX; x >= minX; x--) {
ll xk = power(x);
if (rem - xk < T) break;
if ((unsigned long)x >= (unsigned long)h && T[(unsigned long)x] - T[(unsigned long)x - h] < rem) break;
xs.push_back(x); collect_stat(rem - xk, h - 1, x, xs, states, n); xs.pop_back();
}
}
bool search_from_state(ll rem, int h, ll prevX, vector<ll>& xs) {
if (h == 0) return rem == 0;
if (rem < T) return false;
ll upper = rem - T; if (upper <= 0) return false;
ll maxX = (ll)(pow((double)upper, 1.0 / k)) + 1;
while (maxX > 0 && (unsigned long)maxX < T.size() && power(maxX) > upper) maxX--;
if (maxX >= prevX) maxX = prevX - 1;
ll minX = h; if (minX > maxX) return false;
for (ll x = maxX; x >= minX; x--) {
ll xk = power(x);
if (rem - xk < T) break;
if ((unsigned long)x >= (unsigned long)h && T[(unsigned long)x] - T[(unsigned long)x - h] < rem) break;
if (k == 6 && (unsigned long)x <= 49 && h > 1) {
int xMod = ((long)x % 7 == 0) ? 0 : 1;
int r = (rem - xMod + 7) % 7;
if (!canAchieveMod7(x, h, r)) continue;
} else if((k == 8 || k == 4) && (unsigned long)x <= 25 && h > 1) {
int xMod = ((long)x % 5 == 0) ? 0 : 1;
int r = (rem - xMod + 5) % 5;
if (!canAchieveMod5(x, h, r)) continue;
}
if(k==8 && h>1){
int xMod = ((long)x%2==0)?0:1;
int r = (rem - xMod +32)%32;
if(!canAchieveMod32(x,h,r))continue;
}
if (k == 8 && (unsigned long)x <= 85 && h > 2) {
int xMod = ((long)x % 17 == 0) ? 0 : (pow8mod17[(int)((long)x % 17)] == 1 ? 1 : -1);
ll newRem = rem - xMod;
if (!canAchieveMod17(x, h - 1, newRem)) continue;
}
xs.push_back(x);
if (search_from_state(rem - xk, h - 1, x, xs)) return true;
xs.pop_back();
}
return false;
}
struct Chunk { ll m; int chunk_id; vector<State> states; };
struct Worker { pid_t pid; ll m; int chunk_id; };
string results_dir;
ll parse_ll(const char* s) {
ll n = 0; bool neg = false;
while (*s == ' ' || *s == '\t') s++;
if (*s == '-') { neg = true; s++; }
while (*s >= '0' && *s <= '9') { n = n * 10 + (*s - '0'); s++; }
return neg ? -n : n;
}
int main(int argc, char* argv[]) {
if (argc < 6) {
cerr << "Usage: " << argv << " k n m_start num_processes seed " << endl;
return 1;
}
k = atoi(argv); n = atoi(argv);
ll m_start = parse_ll(argv); int num_processes = atoi(argv); int seed = atoi(argv);
ll m_end = (argc > 6) ? parse_ll(argv) : (ll)n + 1000;
if (k == 8) initMod17();
results_dir = "pipeline_results" + to_string(n);
if (n < 3) { cerr << "Error: n must be >= 3" << endl; return 1; }
initT((unsigned long)m_end);
string rm_cmd = "rm -rf " + results_dir;
system(rm_cmd.c_str());
mkdir(results_dir.c_str(), 0777);
cerr << "Configuration: k=" << k << ", n=" << n << ", m_start=" << m_start
<< ", m_end=" << m_end << ", num_processes=" << num_processes << ", seed=" << seed << endl;
time_t start_time = time(NULL);
ll total_states = 0;
ll best_m = -1;
vector<ll> best_solution;
ll next_m_to_prepare = m_start;
vector<Chunk> chunks;
queue<int> pending_chunks;
map<ll, int> chunks_for_m;
map<pid_t, Worker> working_pids;
auto prepare_next_m = [&]() {
if (best_m > 0 && next_m_to_prepare >= best_m) return;
if (next_m_to_prepare > m_end) return;
ensureT((unsigned long)next_m_to_prepare + 100);
ll mk = power(next_m_to_prepare);
if (mk < T) { next_m_to_prepare++; return; }
vector<State> m_states; vector<ll> xs;
collect_stat(mk, n, next_m_to_prepare, xs, m_states, n);
if (m_states.empty()) { next_m_to_prepare++; return; }
srand(seed + (int)next_m_to_prepare);
random_shuffle(m_states.begin(), m_states.end());
total_states += m_states.size();
int num_chunks = min((int)m_states.size(), num_processes);
int chunk_size = m_states.size() / num_chunks;
int remainder = m_states.size() % num_chunks;
chunks_for_m = num_chunks;
int offset = 0;
for (int i = 0; i < num_chunks; i++) {
int start_idx = offset;
int end_idx = offset + chunk_size + (i < remainder ? 1 : 0);
offset = end_idx;
Chunk c; c.m = next_m_to_prepare; c.chunk_id = i;
c.states.assign(m_states.begin() + start_idx, m_states.begin() + end_idx);
chunks.push_back(c); pending_chunks.push(chunks.size() - 1);
}
cerr << "Prepared " << m_states.size() << " states for m=" << next_m_to_prepare << endl;
next_m_to_prepare++;
};
auto spawn_worker = [&]() {
if (pending_chunks.empty()) {
return false;
}
int chunk_idx = pending_chunks.front(); pending_chunks.pop();
Chunk& chunk = chunks;
pid_t pid = fork();
if (pid == 0) {
bool found = false; vector<ll> xs;
int states_processed = 0;
for (State& s : chunk.states) {
states_processed++;
xs.clear(); xs.push_back(s.x3); xs.push_back(s.x2); xs.push_back(s.x1);
if (search_from_state(s.remaining, n - 3, s.x1, xs)) {
char fname;
sprintf(fname, "%s/m%ld_chunk%d.txt", results_dir.c_str(), (long)chunk.m, chunk.chunk_id);
ofstream fout(fname);
fout << "FOUND m=" << chunk.m << "\n";
fout << "Solution: ";
for (ll x : xs) fout << x << " ";
fout << "\nCount: " << xs.size() << "\n";
fout << "States_processed: " << states_processed << "\n";
fout.close();
found = true;
break;
}
}
if (!found) {
char fname;
sprintf(fname, "%s/complete_m%ld_chunk%d.txt", results_dir.c_str(), (long)chunk.m, chunk.chunk_id);
ofstream fout(fname);
fout << "NO_SOLUTION\n";
fout << "Chunk: " << chunk.chunk_id << "\n";
fout << "States_processed: " << states_processed << "\n";
fout.close();
}
_exit(0);
} else if (pid > 0) {
Worker w; w.pid = pid; w.m = chunk.m; w.chunk_id = chunk.chunk_id;
working_pids=w;
cerr << "Start m="<<w.m<<", chunk_id="<<w.chunk_id<<", pid="<<pid<<endl;
return true;
}
return false;
};
auto scan_results = [&]() {
DIR* dir = opendir(results_dir.c_str());
if (!dir) return;
struct dirent* entry;
while ((entry = readdir(dir)) != NULL) {
if (entry->d_name == 'm' && strstr(entry->d_name, "_chunk") != NULL && strstr(entry->d_name, ".txt") != NULL) {
string ename(entry->d_name);
size_t pos = ename.find('_');
if (pos == string::npos) continue;
string mstr = ename.substr(1, pos-1);
ll file_m = parse_ll(mstr.c_str());
if (file_m > 0 && (best_m < 0 || file_m < best_m)) {
best_m = file_m;
char fullpath;
sprintf(fullpath, "%s/%s", results_dir.c_str(), entry->d_name);
ifstream fin(fullpath);
string line;
while (getline(fin, line)) {
if (line.find("Solution:") == 0) {
istringstream iss(line.substr(9));
best_solution.clear();
ll x;
while (iss >> x) best_solution.push_back(x);
}
}
fin.close();
cerr << "Found m=" << best_m << endl;
}
}
}
closedir(dir);
};
auto kill_workers_ge = [&](ll m_threshold) {
cerr << "Killing workers with m >= " << m_threshold << endl;
for (auto it = working_pids.begin();it!=working_pids.end();){
auto nit = it;++nit;
if(it->second.m>=m_threshold){
kill(it->second.pid, SIGKILL);
working_pids.erase(it);
}
it=nit;
}
};
auto clear_pending_ge = [&](ll m_threshold) {
queue<int> new_pending;
while (!pending_chunks.empty()) {
int idx = pending_chunks.front(); pending_chunks.pop();
if (chunks.m < m_threshold) new_pending.push(idx);
}
pending_chunks = new_pending;
};
auto remove_exited_workers = [&]() {
for (auto it=working_pids.begin(); it!=working_pids.end(); ) {
auto nit = it;++nit;
int status;
pid_t result = waitpid(it->second.pid, &status, WNOHANG);
if (result > 0) {
working_pids.erase(it);
}
it=nit;
}
};
time_t last_progress = 0;
while (true) {
remove_exited_workers();
scan_results();
if (best_m > 0) {
kill_workers_ge(best_m);
clear_pending_ge(best_m);
}
while (working_pids.size() < (size_t)num_processes && !pending_chunks.empty()) {
spawn_worker();
}
if (pending_chunks.empty()) {
if (next_m_to_prepare > m_end) {
if (working_pids.empty()) break;
} else if (best_m > 0 && next_m_to_prepare >= best_m) {
if (working_pids.empty()) break;
} else {
prepare_next_m();
}
}
if (working_pids.empty() && pending_chunks.empty()) {
if (next_m_to_prepare > m_end) break;
if (best_m > 0 && next_m_to_prepare >= best_m) break;
}
time_t now = time(NULL);
if (now - last_progress >= 300) {
last_progress = now;
cerr << "Progress: next_m=" << next_m_to_prepare
<< ", workers=" << working_pids.size()
<< ", pending=" << pending_chunks.size()
<< ", best_m=" << best_m << endl;
}
usleep(10000);
}
for (auto& w : working_pids) {
kill(w.second.pid, SIGKILL);
}
scan_results();
time_t end_time = time(NULL);
double total_time = (double)(end_time - start_time) ;
ofstream summary(results_dir + "/summary.txt");
summary << "Total_time: " << total_time << "s\n";
summary << "Total_states: " << total_states << "\n";
if (best_m > 0) {
summary << "Best_m: " << best_m << "\n";
summary << "Solution: ";
for (ll x : best_solution) summary << x << " ";
summary << "\n";
} else {
summary << "Best_m: NO_SOLUTION\n";
}
summary.close();
if (best_m > 0) {
char dest;
sprintf(dest, "result_n%d_m%ld.txt", n, (long)best_m);
DIR* dir = opendir(results_dir.c_str());
if (dir) {
struct dirent* entry;
while ((entry = readdir(dir)) != NULL) {
if (entry->d_name == 'm') {
string ename(entry->d_name);
size_t pos = ename.find('_');
if (pos == string::npos) continue;
string mstr = ename.substr(1, pos-1);
ll file_m = parse_ll(mstr.c_str());
if (file_m == best_m) {
char src;
sprintf(src, "%s/%s", results_dir.c_str(), entry->d_name);
ifstream fin(src);
ofstream fout(dest);
fout << fin.rdbuf();
fin.close();
fout.close();
break;
}
}
}
closedir(dir);
}
cout << "FOUND " << best_m << " ";
for (ll x : best_solution) cout << x << " ";
cout << endl;
} else {
cout << "NO_SOLUTION" << endl;
}
cerr << "Total_time: " << total_time << "s" << endl;
cerr << "Total_states: " << total_states << endl;
return (best_m > 0) ? 0 : 1;
}
10次幂计算就更加困难了，现在已有数据
n=15,m=166
155 146 139 117 109 92 84 77 70 66 61 53 48 33 14
n=16, m=93
88 81 73 67 66 59 51 45 42 40 39 33 26 23 22 20
n=17,m=119
110 104 95 91 89 88 67 66 57 53 52 51 44 36 22 19 17
n=18,m=131
119 112 109 105 102 90 88 78 77 75 66 64 46 41 39 33 22 11
n=19,m=112
104 99 90 86 77 72 68 63 60 55 48 44 35 33 27 26 22 11 6
n=20,m=140
132 121 110 103 102 96 86 77 66 55 54 52 44 38 34 33 24 19 13 7
n=21,m=144
132 129 117 110 104 88 86 79 66 64 62 55 53 50 44 33 31 30 22 11 8
n=23,m=63
62 51 40 38 37 36 30 28 27 26 25 21 20 17 16 15 12 8 6 5 4 2 1
n=25,m=63
59 53 51 48 47 43 42 41 37 35 33 31 26 25 23 22 20 19 18 17 14 9 6 5 1
本帖最后由 northwolves 于 2026-4-28 22:49 编辑
{22}88^10=83^10+80^10+63^10+54^10+52^10+51^10+48^10+46^10+42^10+40^10+34^10+26^10+25^10+24^10+16^10+15^10+12^10+10^10+8^10+7^10+3^10+1^10
{23}63^10=62^10+51^10+40^10+38^10+37^10+36^10+30^10+28^10+27^10+26^10+25^10+21^10+20^10+17^10+16^10+15^10+12^10+8^10+6^10+5^10+4^10+2^10+1^10
{24}68^10=60^10+58^10+56^10+54^10+53^10+52^10+49^10+48^10+47^10+42^10+41^10+40^10+35^10+34^10+33^10+26^10+24^10+20^10+16^10+15^10+13^10+12^10+4^10+2^10
{25}63^10=59^10+53^10+51^10+48^10+47^10+43^10+42^10+41^10+37^10+35^10+33^10+31^10+26^10+25^10+23^10+22^10+20^10+19^10+18^10+17^10+14^10+9^10+6^10+5^10+1^10
{26}63^10=61^10+48^10+47^10+46^10+45^10+44^10+43^10+39^10+38^10+37^10+36^10+35^10+33^10+31^10+29^10+28^10+23^10+21^10+20^10+18^10+15^10+14^10+13^10+11^10+7^10+5^10
{27}65^10=60^10+55^10+54^10+49^10+48^10+46^10+44^10+43^10+42^10+40^10+37^10+35^10+34^10+33^10+32^10+31^10+30^10+26^10+24^10+23^10+22^10+14^10+12^10+8^10+4^10+2^10+1^10
{28}70^10=65^10+60^10+55^10+53^10+51^10+50^10+49^10+47^10+45^10+44^10+42^10+40^10+37^10+33^10+31^10+28^10+26^10+25^10+22^10+19^10+18^10+15^10+14^10+12^10+11^10+9^10+8^10+1^10
{29}76^10=68^10+67^10+66^10+56^10+55^10+54^10+47^10+46^10+44^10+43^10+39^10+34^10+33^10+29^10+27^10+25^10+23^10+22^10+17^10+16^10+12^10+11^10+10^10+9^10+8^10+7^10+5^10+4^10+1^10
{30}81^10=77^10+67^10+66^10+60^10+55^10+54^10+53^10+49^10+45^10+44^10+42^10+41^10+40^10+37^10+36^10+34^10+33^10+32^10+31^10+24^10+22^10+19^10+17^10+13^10+11^10+10^10+9^10+7^10+2^10+1^10
{31}92^10=88^10+77^10+75^10+66^10+55^10+54^10+53^10+52^10+50^10+49^10+46^10+44^10+41^10+40^10+35^10+33^10+32^10+31^10+30^10+29^10+28^10+27^10+23^10+22^10+21^10+12^10+11^10+8^10+7^10+6^10+1^10
{32}103^10=99^10+88^10+77^10+73^10+68^10+66^10+55^10+53^10+52^10+51^10+44^10+43^10+42^10+41^10+40^10+39^10+37^10+33^10+30^10+24^10+22^10+21^10+20^10+16^10+13^10+11^10+7^10+6^10+5^10+4^10+2^10+1^10
{33}77^10=74^10+62^10+59^10+56^10+54^10+53^10+50^10+49^10+47^10+46^10+45^10+43^10+42^10+38^10+37^10+36^10+35^10+28^10+25^10+24^10+23^10+21^10+20^10+19^10+18^10+17^10+16^10+13^10+8^10+5^10+4^10+3^10+1^10
{34}72^10=68^10+61^10+58^10+54^10+48^10+47^10+46^10+45^10+43^10+42^10+41^10+40^10+38^10+37^10+35^10+34^10+31^10+30^10+29^10+28^10+26^10+25^10+24^10+23^10+21^10+20^10+17^10+15^10+14^10+13^10+12^10+9^10+8^10+4^10
{35}71^10=64^10+60^10+59^10+58^10+54^10+51^10+49^10+48^10+45^10+42^10+39^10+38^10+37^10+36^10+35^10+33^10+32^10+31^10+29^10+28^10+26^10+21^10+20^10+19^10+18^10+17^10+14^10+13^10+12^10+10^10+9^10+8^10+7^10+5^10+4^10
{36}67^10=59^10+57^10+56^10+53^10+52^10+50^10+49^10+47^10+45^10+44^10+42^10+38^10+37^10+36^10+34^10+30^10+29^10+28^10+27^10+26^10+23^10+22^10+21^10+20^10+18^10+17^10+16^10+14^10+13^10+10^10+9^10+7^10+6^10+4^10+3^10+1^10
{37}65^10=60^10+56^10+53^10+49^10+48^10+45^10+44^10+42^10+41^10+40^10+38^10+36^10+34^10+33^10+32^10+31^10+30^10+28^10+24^10+21^10+20^10+19^10+18^10+17^10+15^10+14^10+13^10+12^10+11^10+9^10+8^10+7^10+6^10+5^10+3^10+2^10+1^10
{38}65^10=59^10+56^10+53^10+50^10+48^10+47^10+46^10+45^10+44^10+41^10+40^10+38^10+36^10+33^10+32^10+31^10+28^10+27^10+26^10+24^10+23^10+22^10+21^10+17^10+16^10+15^10+14^10+13^10+12^10+11^10+10^10+8^10+7^10+6^10+5^10+4^10+2^10+1^10
{39}74^10=66^10+62^10+60^10+59^10+57^10+55^10+54^10+53^10+50^10+49^10+48^10+46^10+45^10+44^10+42^10+41^10+40^10+38^10+34^10+33^10+31^10+30^10+29^10+28^10+27^10+26^10+24^10+23^10+22^10+20^10+19^10+13^10+12^10+10^10+8^10+6^10+4^10+3^10+1^10
{40}74^10=66^10+65^10+60^10+57^10+55^10+54^10+52^10+51^10+49^10+48^10+47^10+46^10+44^10+41^10+40^10+39^10+38^10+35^10+34^10+33^10+32^10+31^10+30^10+28^10+27^10+26^10+24^10+23^10+22^10+21^10+20^10+18^10+16^10+14^10+13^10+12^10+11^10+8^10+6^10+2^10
{41}82^10=77^10+68^10+66^10+62^10+60^10+56^10+55^10+54^10+53^10+52^10+48^10+46^10+44^10+43^10+42^10+40^10+39^10+38^10+36^10+33^10+32^10+27^10+26^10+25^10+24^10+22^10+21^10+20^10+19^10+18^10+17^10+16^10+15^10+14^10+13^10+12^10+11^10+9^10+6^10+2^10+1^10
{42}92^10=88^10+77^10+70^10+66^10+65^10+61^10+59^10+58^10+55^10+53^10+52^10+49^10+47^10+46^10+45^10+44^10+42^10+41^10+40^10+39^10+37^10+34^10+33^10+30^10+29^10+23^10+22^10+21^10+19^10+18^10+17^10+15^10+13^10+11^10+10^10+8^10+6^10+5^10+4^10+3^10+2^10+1^10
{43}103^10=99^10+88^10+77^10+72^10+66^10+63^10+59^10+58^10+57^10+56^10+55^10+52^10+51^10+50^10+49^10+47^10+45^10+44^10+43^10+41^10+40^10+39^10+37^10+34^10+33^10+32^10+29^10+27^10+25^10+24^10+22^10+21^10+19^10+18^10+16^10+15^10+12^10+11^10+10^10+7^10+5^10+2^10+1^10
{44} 115^10=110^10+99^10+88^10+82^10+77^10+66^10+63^10+62^10+61^10+58^10+56^10+55^10+54^10+51^10+50^10+49^10+48^10+47^10+45^10+44^10+42^10+40^10+37^10+36^10+34^10+33^10+32^10+30^10+29^10+28^10+26^10+24^10+22^10+21^10+20^10+19^10+18^10+16^10+12^10+11^10+10^10+3^10+2^10+1^10
{45}84^10=74^10+71^10+70^10+69^10+64^10+62^10+61^10+57^10+56^10+53^10+52^10+51^10+48^10+47^10+46^10+43^10+42^10+41^10+40^10+35^10+34^10+32^10+31^10+29^10+28^10+27^10+26^10+25^10+23^10+21^10+20^10+19^10+18^10+17^10+16^10+15^10+13^10+12^10+10^10+7^10+6^10+5^10+4^10+3^10+1^10
{46}79^10=74^10+64^10+61^10+60^10+58^10+57^10+56^10+55^10+54^10+53^10+51^10+48^10+47^10+45^10+43^10+42^10+39^10+38^10+37^10+36^10+35^10+32^10+31^10+29^10+28^10+27^10+26^10+25^10+24^10+23^10+21^10+20^10+19^10+18^10+17^10+16^10+15^10+14^10+13^10+12^10+9^10+7^10+6^10+4^10+3^10+1^10
{47}79^10=71^10+67^10+65^10+62^10+60^10+58^10+55^10+53^10+52^10+51^10+50^10+49^10+48^10+47^10+46^10+45^10+44^10+43^10+42^10+40^10+39^10+38^10+37^10+36^10+35^10+34^10+31^10+29^10+28^10+26^10+25^10+23^10+21^10+20^10+19^10+16^10+15^10+14^10+13^10+12^10+10^10+9^10+7^10+6^10+5^10+4^10+3^10
{48}77^10=65^10+64^10+63^10+62^10+61^10+60^10+58^10+57^10+55^10+54^10+52^10+49^10+48^10+45^10+44^10+43^10+41^10+40^10+39^10+38^10+37^10+36^10+35^10+34^10+33^10+32^10+31^10+29^10+28^10+26^10+25^10+23^10+22^10+21^10+20^10+19^10+18^10+17^10+16^10+13^10+12^10+9^10+7^10+6^10+5^10+4^10+2^10+1^10
{49}78^10=71^10+67^10+62^10+60^10+59^10+57^10+56^10+53^10+52^10+49^10+48^10+46^10+45^10+44^10+43^10+41^10+40^10+38^10+37^10+36^10+35^10+34^10+33^10+32^10+30^10+29^10+28^10+26^10+25^10+24^10+23^10+22^10+21^10+20^10+17^10+16^10+14^10+13^10+12^10+11^10+9^10+8^10+7^10+6^10+5^10+4^10+3^10+2^10+1^10
{50}82^10=70^10+69^10+67^10+65^10+64^10+63^10+60^10+59^10+58^10+56^10+55^10+54^10+53^10+52^10+51^10+50^10+49^10+48^10+47^10+45^10+44^10+42^10+41^10+40^10+38^10+36^10+35^10+33^10+32^10+31^10+29^10+27^10+26^10+25^10+24^10+23^10+22^10+20^10+18^10+17^10+16^10+15^10+14^10+12^10+11^10+10^10+8^10+7^10+6^10+5^10
{51}80^10=69^10+68^10+66^10+63^10+62^10+59^10+58^10+57^10+56^10+55^10+54^10+53^10+52^10+51^10+49^10+48^10+46^10+44^10+42^10+40^10+39^10+38^10+37^10+36^10+35^10+34^10+33^10+32^10+31^10+30^10+29^10+28^10+27^10+25^10+24^10+23^10+22^10+21^10+20^10+19^10+18^10+15^10+14^10+11^10+10^10+9^10+8^10+6^10+5^10+3^10+2^10
{52}86^10=77^10+75^10+68^10+66^10+64^10+63^10+61^10+60^10+58^10+56^10+55^10+54^10+53^10+52^10+51^10+50^10+49^10+48^10+47^10+44^10+43^10+42^10+41^10+40^10+36^10+35^10+34^10+33^10+31^10+30^10+29^10+28^10+26^10+25^10+24^10+23^10+22^10+19^10+18^10+16^10+15^10+13^10+12^10+11^10+10^10+9^10+8^10+6^10+5^10+4^10+3^10+2^10
{53} >=86
{54} >=86
{55} >=88
{56} >=89
{57} >=90
{58} 93^10=80^10+78^10+76^10+74^10+72^10+70^10+68^10+67^10+65^10+64^10+63^10+62^10+61^10+60^10+58^10+57^10+56^10+54^10+53^10+51^10+48^10+46^10+45^10+44^10+42^10+40^10+39^10+38^10+37^10+36^10+35^10+32^10+30^10+28^10+27^10+26^10+25^10+24^10+23^10+21^10+20^10+19^10+18^10+17^10+16^10+15^10+14^10+13^10+12^10+11^10+10^10+9^10+7^10+6^10+5^10+4^10+3^10+1^10
{59} >=93
{60} 94^10=84^10+77^10+74^10+73^10+71^10+70^10+69^10+67^10+66^10+65^10+64^10+63^10+62^10+61^10+60^10+59^10+57^10+56^10+55^10+53^10+52^10+51^10+50^10+49^10+48^10+47^10+45^10+43^10+42^10+41^10+38^10+35^10+34^10+32^10+31^10+30^10+29^10+28^10+27^10+26^10+25^10+24^10+23^10+20^10+19^10+18^10+16^10+15^10+14^10+13^10+12^10+11^10+10^10+9^10+8^10+7^10+5^10+4^10+2^10+1^10
{61} 96^10=86^10+81^10+78^10+75^10+72^10+71^10+69^10+68^10+66^10+64^10+63^10+60^10+59^10+57^10+56^10+55^10+53^10+52^10+51^10+50^10+49^10+48^10+47^10+46^10+45^10+44^10+43^10+42^10+41^10+40^10+39^10+38^10+37^10+36^10+34^10+32^10+31^10+30^10+29^10+28^10+27^10+26^10+24^10+23^10+22^10+21^10+20^10+19^10+18^10+17^10+15^10+13^10+12^10+11^10+9^10+8^10+7^10+6^10+5^10+3^10+1^10
{62} 95^10=85^10+81^10+78^10+74^10+71^10+69^10+66^10+65^10+64^10+63^10+62^10+61^10+60^10+58^10+57^10+55^10+53^10+52^10+50^10+49^10+48^10+47^10+46^10+45^10+44^10+43^10+42^10+41^10+40^10+39^10+38^10+37^10+36^10+35^10+34^10+33^10+30^10+29^10+27^10+26^10+25^10+23^10+22^10+21^10+20^10+19^10+18^10+17^10+16^10+15^10+14^10+13^10+12^10+11^10+10^10+9^10+7^10+6^10+5^10+4^10+3^10+2^10
{63} 96^10=85^10+79^10+77^10+76^10+75^10+72^10+71^10+68^10+66^10+65^10+64^10+63^10+62^10+61^10+59^10+57^10+56^10+55^10+53^10+52^10+50^10+49^10+48^10+47^10+46^10+45^10+44^10+43^10+42^10+40^10+39^10+38^10+36^10+35^10+33^10+32^10+31^10+29^10+28^10+26^10+25^10+24^10+23^10+22^10+21^10+20^10+19^10+18^10+17^10+16^10+15^10+14^10+13^10+12^10+11^10+10^10+9^10+8^10+7^10+6^10+4^10+2^10+1^10
{64} >=97
{65} >=98
{66} >=99
{67} >=101
{68} >=101
{69} >=103
{70} >=104
{71} >=105
{72} >=101
{73} >=107
{74} >=108
{75} >=108
{76} >=109
{77} >=110
{78} >=112
{79} >=113
{80} >=115
10次幂，
n=14,m=172
157 151 141 133 129 126 110 83 68 44 37 32 31 12
mathe 发表于 2026-4-28 20:09
10次幂，
n=14,m=172
157 151 141 133 129 126 110 83 68 44 37 32 31 12
10次幂，n=44, 找到一组解：m=115
115^10=110^10+99^10+88^10+82^10+77^10+66^10+63^10+62^10+61^10+58^10+56^10+55^10+54^10+51^10+50^10+49^10+48^10+47^10+45^10+44^10+42^10+40^10+37^10+36^10+34^10+33^10+32^10+30^10+29^10+28^10+26^10+24^10+22^10+21^10+20^10+19^10+18^10+16^10+12^10+11^10+10^10+3^10+2^10+1^10
现在的问题是m=99 和m=110 有没有解呢？