不同正整数之和

白新岭 · 发表于 2021-11-4 23:42:27

它们的解组数与多项式at^3+bt^2+ct+d应该相关联，这里的t为周期值，每个循环周期为4，a，b，c，d是需要待求系数。

白新岭 · 发表于 2021-11-4 23:49:33

本帖最后由白新岭于 2021-11-5 08:17 编辑

mod(n,4) 6at^3 6bt^2 6ct d
1→→→ 3 -18 33 -3
2→→→ 2 -9 13 -1
3→→→ 3 -15 24 -2
4→→→ 3 -12 15 -1

白新岭 · 发表于 2021-11-4 23:52:11

125周 126周 127周
930372 953250 976500
627874 643250 658875
937998 961000 984375
945624 968750 992250
945624（500）+643250（502）=1588874结果有出入，与1694777.不知道错在何处？

王守恩 · 发表于 2021-11-5 07:48:06

白新岭发表于 2021-11-4 23:37
n值王守恩白新岭出入
10  1 1 0
11  1 1 0

23楼=14楼，肯定是没问题的。
10=01:{1,2,3,4}
11=01:{1,2,3,5}
12=02:{1,2,3,6},{1,2,4,5}
13=03:{1,2,3,7},{1,2,4,6},{1,3,4,5}
14=05:{1,2,3,8},{1,2,4,7},{1,2,5,6},{1,3,4,6},{2,3,4,5}
15=06:{1,2,3,9},{1,2,4,8},{1,2,5,7},{1,3,4,7},{1,3,5,6},{2,3,4,6}
16=09:{1,2,3,0},{1,2,4,9},{1,2,5,8},{1,2,6,7},{1,3,4,8},{1,3,5,7},{1,4,5,6},{2,3,4,7},{2,3,5,6}
17=11:{1,2,3,1},{1,2,4,0},{1,2,5,9},{1,2,6,8},{1,3,4,9},{1,3,5,8},{1,3,6,7},{1,4,5,7},{2,3,4,8},{2,3,5,7},{2,4,5,6}
18=15:{1,2,3,2},{1,2,4,1},{1,2,5,0},{1,2,6,9},{1,2,7,8},{1,3,4,0},{1,3,5,9},{1,3,6,8},{1,4,5,8},{1,4,6,7},{2,3,4,9},{2,3,5,8},{2,3,6,7},{2,4,5,7},{3,4,5,6}
19=18:{1,2,3,3},{1,2,4,2},{1,2,5,1},{1,2,6,0},{1,2,7,9},{1,3,4,1},{1,3,5,0},{1,3,6,9},{1,3,7,8},{1,4,5,9},{1,4,6,8},{1,5,6,7},{2,3,4,0},{2,3,5,9},{2,3,6,8},{2,4,5,8},{2,4,6,7},{3,4,5,7}
20=23:{1,2,3,4},{1,2,4,3},{1,2,5,2},{1,2,6,1},{1,2,7,0},{1,2,8,9},{1,3,4,2},{1,3,5,1},{1,3,6,0},{1,3,7,9},{1,4,5,0},{1,4,6,9},{1,4,7,8},{1,5,6,8},{2,3,4,1},{2,3,5,0},{2,3,6,9},{2,3,7,8},
      {2,4,5,9},{2,4,6,8},{2,5,6,7},{3,4,5,8},{3,4,6,7}
21=27:{1,2,3,5},{1,2,4,4},{1,2,5,3},{1,2,6,2},{1,2,7,1},{1,2,8,0},{1,3,4,3},{1,3,5,2},{1,3,6,1},{1,3,7,0},{1,3,8,9},{1,4,5,1},{1,4,6,0},{1,4,7,9},{1,4,6,8},{1,5,6,9},{1,5,7,8},{2,3,4,2},
      {2,3,5,1},{2,3,6,0},{2,3,7,9},{2,4,5,0},{2,4,6,9},{2,4,7,8},{2,5,6,8},{3,4,5,9},{3,4,6,8}
22=34:{1,2,3,6},{1,2,4,5},{1,2,5,4},{1,2,6,3},{1,2,7,2},{1,2,8,1},{1,2,9,0},{1,3,4,4},{1,3,5,3},{1,3,6,2},{1,3,7,1},{1,3,8,0},{1,4,5,2},{1,4,6,1},{1,4,7,0},{1,4,8,9},{1,5,6,9},{1,5,6,0},
      {1,5,7,9},{1,6,7,8},{2,3,4,3},{2,3,5,2},{2,3,6,1},{2,3,7,0},{2,3,8,9},{2,4,5,1},{2,4,6,0},{2,4,7,9},{2,5,6,9},{2,5,7,8},{3,4,5,0},{3,4,6,9},{3,4,7,8},{3,5,6,8}
23=39:{1,2,3,7},{1,2,4,6},{1,2,5,5},{1,2,6,4},{1,2,7,3},{1,2,8,2},{1,2,9,1},{},{}
24=47:{1,2,3,8},{1,2,4,7},{1,2,5,6},{1,2,6,5},{1,2,7,4},{1,2,8,3},{1,2,9,2},{},{}
25=54:{1,2,3,9},{1,2,4,8},{1,2,5,7},{1,2,6,6},{1,2,7,5}
26=64:{1,2,3,0},{1,2,4,9},{1,2,5,8},{1,2,6,7},{1,2,7,6}

白新岭 · 发表于 2021-11-5 07:59:13

本帖最后由白新岭于 2021-11-5 08:17 编辑

mod(n,24) 6at^3 6bt^2 6ct d 1周 21周 n值
1→→→ 576 -2016 2340 -150 0 748920 481
2→→→ 576 -1944 2184 -136 0 753680 482
3→→→ 576 -1872 2016 -120 0 758400 483
4→→→ 576 -1800 1872 -108 0 763200 484
5→→→ 576 -1728 1716 -94 0 767960 485
6→→→ 576 -1656 1584 -84 0 772800 486
7→→→ 576 -1584 1440 -72 0 777600 487
8→→→ 576 -1512 1320 -64 0 782480 488
9→→→ 576 -1440 1188 -54 0 787320 489
10→→→ 576 -1368 1080 -47 1 792241 490
11→→→ 576 -1296 960 -39 1 797121 491
12→→→ 576 -1224 864 -34 2 802082 492
13→→→ 576 -1152 756 -27 3 807003 493
14→→→ 576 -1080 672 -23 5 812005 494
15→→→ 576 -1008 576 -18 6 816966 495
16→→→ 576 -936 504 -15 9 822009 496
17→→→ 576 -864 420 -11 11 827011 497
18→→→ 576 -792 360 -9 15 832095 498
19→→→ 576 -720 288 -6 18 837138 499
20→→→ 576 -648 240 -5 23 842263 500
21→→→ 576 -576 180 -3 27 847347 501
22→→→ 576 -504 144 -2 34 852514 502
23→→→ 576 -432 96 -1 39 857639 503
24→→→ 576 -360 72 -1 47 862847 504

白新岭 · 发表于 2021-11-5 08:00:42

套用上楼公式可以求出任意n值的，符合条件的表法数。

白新岭 · 发表于 2021-11-5 08:22:21

本帖最后由白新岭于 2021-11-5 08:23 编辑

白新岭发表于 2021-11-5 07:59
mod(n,24) 6at^3 6bt^2 6ct d 1周 21周 n值
1→→→ 576 -2016 2340 -150 0 748920 481
2→→→ 576 -194 ...

mod(n,24) at^3 bt^2 ct d 1周 21周 n值
1→→→ 96 -336 390 -150 0 748920 481
2→→→ 96 -324 364 -136 0 753680 482
3→→→ 96 -312 336 -120 0 758400 483
4→→→ 96 -300 312 -108 0 763200 484
5→→→ 96 -288 286 -94 0 767960 485
6→→→ 96 -276 264 -84 0 772800 486
7→→→ 96 -264 240 -72 0 777600 487
8→→→ 96 -252 220 -64 0 782480 488
9→→→ 96 -240 198 -54 0 787320 489
10→→→ 96 -228 180 -47 1 792241 490
11→→→ 96 -216 160 -39 1 797121 491
12→→→ 96 -204 144 -34 2 802082 492
13→→→ 96 -192 126 -27 3 807003 493
14→→→ 96 -180 112 -23 5 812005 494
15→→→ 96 -168 96 -18 6 816966 495
16→→→ 96 -156 84 -15 9 822009 496
17→→→ 96 -144 70 -11 11 827011 497
18→→→ 96 -132 60 -9 15 832095 498
19→→→ 96 -120 48 -6 18 837138 499
20→→→ 96 -108 40 -5 23 842263 500
21→→→ 96 -96 30 -3 27 847347 501
22→→→ 96 -84 24 -2 34 852514 502
23→→→ 96 -72 16 -1 39 857639 503
24→→→ 96 -60 12 -1 47 862847 504
那楼是套用以前的方法，系数没有简化，本楼是简化后的数据。

白新岭 · 发表于 2021-11-5 12:11:59

迟到的方法，本主题2014年就发了出来，现在才
注意到，有点过时了。

账号		自动登录	找回密码
密码			欢迎注册

[提问] 不同正整数之和

点评

评分