求\(a^2+ab+b^2=c^k\)的解
其中\\k=3的解答:
Do==1,{a,b,c},Integers]};(*调用reduce函数求解*)
If,(*如果解答存在的话*)
outabc={a,b,c}/.out;(*去掉a->这类符号,只保留结果*)
Map(*通过映射打印出所有解答*)
],
{n,1,400}
]
{1,18,7}
{17,36,13}
{17,73,19}
{90,109,31}
{71,181,37}
{126,197,43}
{37,323,49}
{179,361,61}
{251,378,67}
{216,487,73}
{127,630,79}
{270,701,91}
{359,631,91}
{269,792,97}
{594,613,103}
{307,953,109}
{629,1009,127}
{233,1404,133}
{396,1297,133}
{703,1170,139}
{71,1819,151}
{468,1691,157}
{1007,1386,163}
{1007,1513,169}
{739,1980,181}
{937,2087,193}
{1170,2033,199}
{630,2701,211}
{1511,2161,217}
{1819,1872,217}
{73,3293,223}
{703,3060,229}
{720,3329,241}
{629,3529,247}
{2142,2339,247}
{1097,3510,259}
{1530,3187,259}
{2159,2971,271}
{379,4409,277}
{577,4446,283}
{2071,3869,301}
{2591,3420,301}
{918,4861,307}
{2736,3637,313}
{2969,3961,331}
{811,5741,337}
{1026,5777,343}
{3060,4427,349}
{2771,5040,361}
{1691,6031,367}
{4033,4284,373}
{827,6930,379}
{3959,5149,397}
k=4的解答
{16,39,7}
{15,161,13}
{185,231,19}
{455,649,31}
{511,1040,37}
{1056,1079,43}
{1265,1504,49}
{1089,3055,61}
{1001,3904,67}
{2431,3680,73}
{1001,5680,79}
{1991,7104,91}
{3401,6039,91}
{224,9295,97}
{4329,7760,103}
{5136,8449,109}
{3289,14231,127}
{3519,15665,133}
{6049,13871,133}
{3520,17319,139}
{10089,16016,151}
{7775,19824,157}
{6919,22425,163}
{5055,25696,169}
{209,32656,181}
{12224,29601,193}
{21616,24089,199}
{12151,37184,211}
{7361,42975,217}
{18031,35409,217}
{20999,35785,223}
{6864,48671,229}
{14849,49215,241}
{26320,43431,247}
{34416,36025,247}
{3289,65376,259}
{32384,44745,259}
{10279,67760,271}
{38064,50255,277}
{19175,68761,283}
{23920,76241,301}
{25185,75344,301}
{21385,81719,307}
{49984,62895,313}
{13881,101959,331}
{62959,68145,337}
{25271,102960,343}
{66079,74481,349}
{19136,119695,361}
{63184,91481,367}
{51425,106096,373}
{36105,122144,379}
{18239,147696,397}
k=5的解答
{62,87,7}
{116,543,13}
{93,1525,19}
{1626,4349,31}
{1076,7737,37}
{5257,8609,43}
{3725,14632,49}
{6775,25076,61}
{801,36337,67}
{25559,27009,73}
{27050,36757,79}
{23574,64525,91}
{40049,50950,91}
{30349,73688,97}
{23441,94018,103}
{6293,120775,109}
{62363,142374,127}
{86459,146532,133}
{108407,126909,133}
{16757,218950,139}
{93699,221326,151}
{120899,230113,157}
{8834,334707,163}
{139432,281393,169}
{128325,362351,181}
{97191,461993,193}
{269925,372418,199}
{219449,508425,211}
{128176,620637,217}
{277551,511912,217}
{267641,571693,223}
{360043,549732,229}
{286799,723376,241}
{126401,889362,247}
{238187,817287,247}
{386082,833443,259}
{606407,640018,259}
{507050,872901,271}
{336612,1075001,277}
{776891,778843,283}
{76399,1532276,301}
{423049,1317051,301}
{466649,1367838,307}
{611059,1344957,313}
{866899,1413050,331}
{382213,1867299,337}
{583109,1828009,343}
{899900,1687857,349}
{292299,2316976,361}
{1937,2579301,367}
{449841,2433716,373}
{1579425,1649318,379}
{1405788,2191849,397}
k=6的解答
{37,323,7}
{1007,1513,13}
{2771,5040,19}
{3781,27720,31}
{27720,30743,37}
{22933,65520,43}
{25271,102960,49}
{98280,161279,61}
{79883,252757,67}
{190513,257040,73}
{176149,380771,79}
{269280,581939,91}
{418501,451440,91}
{498457,554903,97}
{22933,1081080,103}
{679391,813960,109}
{622440,1664963,127}
{708553,1916927,133}
{1184040,1525393,133}
{874691,2139229,139}
{263339,3303720,151}
{1801800,2640457,157}
{906947,3805453,163}
{1275120,4061231,169}
{3374279,3472561,181}
{3477600,4789007,193}
{2764189,6126120,199}
{3800160,6898501,211}
{195623,10119097,217}
{2386800,8813663,217}
{486107,10838520,223}
{4796569,8869391,229}
{5312160,10563841,241}
{882757,14608440,247}
{4835123,12058200,247}
{7816069,12093120,259}
{8904349,11116691,259}
{4165560,17490059,271}
{3485663,19295640,277}
{5463613,19433987,283}
{4983119,24435721,301}
{10680120,20314439,301}
{9767520,22786597,307}
{5742073,27387360,313}
{6874560,32335379,331}
{9969623,32301360,337}
{12907080,32321053,343}
{10234729,36456840,349}
{17723159,35610121,361}
{23256323,33513480,367}
{2087567,50819833,373}
{12146149,47340971,379}
{10838520,56443463,397}
奇怪,最后一列似乎是一样的! k=7的解答:
{249,757,7}
{3532,5541,13}
{9578,23935,19}
{8815,161286,31}
{18651,298361,37}
{72078,481573,43}
{438987,511048,49}
{153716,1690915,61}
{1224461,1609533,67}
{1267064,2503873,73}
{90730,4336157,79}
{1294015,6453714,91}
{3315069,4932901,91}
{2322947,7599304,97}
{1955763,9981983,103}
{2300765,12222492,109}
{5632698,19746461,127}
{1290731,26463532,133}
{15595283,15733873,133}
{17788670,18768217,139}
{20205346,28416785,151}
{26063857,29883684,157}
{24113617,39139142,163}
{18227657,51616648,169}
{24701055,64504429,181}
{2224649,98742663,193}
{23682217,97420178,199}
{63900901,92778854,211}
{33487259,130961392,217}
{49028104,119898567,217}
{73294939,116307078,223}
{13211873,174762492,229}
{95558401,153145455,241}
{31466722,219525029,247}
{98794339,171439614,247}
{60173082,244622183,259}
{93054795,221215178,259}
{115754931,254046230,271}
{201297077,207148039,277}
{45576953,356450478,283}
{65348631,437061229,301}
{192422145,346603339,301}
{198601957,377604629,307}
{9711088,537586059,313}
{247733630,500054929,331}
{340160696,467772963,337}
{277555573,568871874,343}
{64619873,759840987,349}
{481146141,550236944,361}
{226368333,813260426,367}
{247118239,855586893,373}
{149194562,977329843,379}
{490815853,926607516,397}
谁能说明一下为什么最后一列的c值都是一样的呢? \ \
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