160313

Ruby

ディオファンタスm-項(2)

D(t) ディオファンタス4-項（ただし、t は3 の倍数）をたくさん見つけるコードを書いてみた。

class Array
  def gcd
    self.inject{|a, b| a.gcd(b)}
  end
end

# 要素がすべて平方数か？
def test(a)
  a.all?{|i| i == Math.sqrt(i).to_i ** 2}
end

n = 20
ary = []
(1..n).each{|p0|
  (1..n).each{|t0|
    (1..n).each{|s0|
      if [p0, t0, s0].gcd == 1
        t = 3 * (p0 - t0 - s0) * (p0 + t0 - s0) * (p0 + s0) * (p0 + s0)
        x =     t0 * t0 + 2 * s0 * s0 + 2 * p0 * s0 -     p0 * p0
        y =     t0 * t0 -     s0 * s0 + 2 * p0 * s0 + 2 * p0 * p0
        z = 4 * t0 * t0 - (p0 - s0) * (p0 - s0)
        q = 3 * (p0 + s0) * (p0 + s0)
        a = [x, y, z, q].sort!
        if a.all?{|i| i > 0}
          if ([t] + a).gcd == 1
            if a == a.uniq
              if test(a.combination(2).map{|c| c[0] * c[1] + t})
                b = [t, a]
                ary << b if !ary.include?(b)
              end
            end
          end
        end
      end
    }
  }
}
p ary.sort

出力結果
[[-1473849, [1295, 1406, 1523, 4563]], [-1445664, [1219, 1435, 1552, 4107]], [-1436925, [1159, 1474, 1591, 3675]], [-1277397, [1066, 1363, 1591, 3267]], [-1244160, [1187, 1292, 1403, 3888]], [-1149984, [1027, 1324, 1435, 3267]], [-1127253, [979, 1258, 1591, 2883]], [-1127100, [913, 1408, 1525, 3468]], [-1118208, [871, 1447, 1564, 3072]], [-1098825, [974, 1271, 1499, 3675]], [-1068144, [983, 1280, 1391, 3468]], [-1055241, [1091, 1190, 1295, 3267]], [-1029000, [1048, 1147, 1363, 3675]], [-1022112, [899, 1307, 1424, 4563]], [-1014816, [940, 1219, 1435, 2883]], [-1014429, [1015, 1114, 1447, 4107]], [-986493, [898, 1159, 1591, 2523]], [-983040, [995, 1187, 1292, 3072]], [-976833, [887, 1271, 1382, 3267]], [-957372, [896, 1193, 1421, 4332]], [-931209, [998, 1091, 1295, 2883]], [-919968, [899, 1196, 1307, 4107]], [-914760, [955, 1147, 1252, 3267]], [-898425, [782, 1247, 1475, 3267]], [-888096, [859, 1120, 1435, 2523]], [-877500, [757, 1297, 1408, 2700]], [-877404, [841, 1120, 1453, 3468]], [-856128, [727, 1231, 1564, 2352]], [-855117, [823, 1066, 1591, 2187]], [-823200, [899, 1091, 1196, 3675]], [-814929, [911, 998, 1295, 2523]], [-812592, [884, 977, 1409, 3888]], [-807240, [643, 1363, 1480, 2883]], [-806949, [922, 1015, 1219, 3267]], [-804837, [619, 1402, 1519, 2523]], [-792825, [707, 1247, 1358, 2883]], [-769824, [784, 1027, 1435, 2187]], [-768009, [775, 1054, 1387, 4107]], [-766428, [896, 989, 1193, 3468]], [-754377, [731, 1166, 1271, 2523]], [-752640, [827, 995, 1292, 2352]], [-733125, [754, 979, 1591, 1875]], [-731808, [899, 992, 1091, 3267]], [-712101, [835, 1015, 1114, 2883]], [-706440, [787, 1048, 1147, 2523]], [-706401, [830, 911, 1295, 2187]], [-702000, [623, 1232, 1343, 2700]], [-697653, [562, 1291, 1519, 2187]], [-675840, [727, 988, 1303, 3072]], [-659100, [625, 1093, 1408, 2028]], [-657120, [667, 1027, 1360, 4107]], [-653913, [662, 1067, 1271, 2187]], [-653400, [788, 875, 1283, 3267]], [-652509, [575, 1226, 1343, 4563]], [-642048, [797, 884, 1181, 3072]], [-628992, [607, 1039, 1564, 1728]], [-624624, [671, 983, 1280, 2028]], [-620517, [691, 898, 1587, 1591]], [-612360, [523, 1252, 1363, 2187]], [-612360, [712, 955, 1147, 2187]], [-610929, [775, 862, 1159, 3267]], [-601425, [575, 1142, 1247, 2187]], [-599664, [571, 1075, 1408, 2883]], [-598125, [511, 1186, 1519, 1875]], [-596700, [809, 896, 989, 2700]], [-588000, [667, 928, 1243, 3675]], [-587301, [575, 1115, 1226, 4107]], [-576600, [707, 875, 1172, 2883]], [-574992, [683, 851, 1376, 3267]], [-560625, [599, 974, 1271, 1875]], [-558624, [652, 859, 1435, 1587]], [-552960, [683, 827, 1292, 1728]], [-544320, [572, 1007, 1223, 3888]], [-540189, [679, 922, 1015, 2187]], [-527280, [503, 1127, 1232, 2028]], [-526848, [467, 1196, 1307, 2352]], [-525000, [472, 1147, 1363, 1875]], [-525000, [643, 868, 1147, 1875]], [-524784, [508, 1075, 1291, 2523]], [-522720, [667, 835, 1132, 3267]], [-517440, [583, 988, 1087, 2352]], [-517293, [634, 823, 1323, 1591]], [-515625, [518, 1043, 1247, 1875]], [-513084, [553, 1021, 1120, 2028]], [-512601, [686, 755, 1295, 1587]], [-512169, [446, 1175, 1403, 2523]], [-510384, [409, 1300, 1417, 2352]], [-507408, [608, 851, 1259, 2883]], [-506253, [466, 1087, 1519, 1587]], [-504600, [632, 875, 1067, 2523]], [-504525, [538, 943, 1375, 2883]], [-494592, [593, 836, 1361, 3072]], [-491568, [641, 884, 977, 2352]], [-491520, [667, 748, 1243, 3072]], [-489888, [731, 812, 899, 2187]], [-474513, [542, 887, 1271, 1587]], [-471801, [694, 775, 955, 2523]], [-467181, [575, 911, 1010, 3267]], [-461280, [667, 748, 1027, 2883]], [-461244, [640, 721, 1333, 3468]], [-459984, [475, 979, 1312, 4107]], [-454896, [451, 1075, 1180, 2187]], [-448188, [653, 809, 896, 2028]], [-447216, [551, 815, 1280, 1452]], [-444360, [427, 1048, 1363, 1587]], [-444360, [580, 787, 1147, 1587]], [-444048, [539, 851, 1148, 2523]], [-443961, [395, 1175, 1286, 2187]], [-443904, [560, 803, 1211, 3468]], [-441525, [475, 943, 1258, 2523]], [-437400, [563, 875, 968, 2187]], [-437325, [551, 794, 1319, 3675]], [-436800, [511, 871, 1200, 1564]], [-436425, [467, 950, 1247, 1587]], [-430080, [572, 815, 1007, 3072]], [-423453, [583, 754, 1083, 1591]], [-420000, [656, 731, 899, 1875]], [-412269, [575, 818, 911, 2883]], [-408969, [619, 775, 862, 2187]], [-395577, [491, 806, 1271, 1323]], [-391989, [547, 754, 1015, 1587]], [-388773, [551, 707, 1202, 3267]], [-387072, [371, 1091, 1196, 1728]], [-384912, [476, 851, 1043, 2187]], [-384000, [563, 683, 1200, 1292]], [-382725, [418, 943, 1147, 2187]], [-381216, [544, 715, 1083, 1435]], [-380160, [463, 895, 988, 1728]], [-378672, [461, 836, 1133, 2352]], [-376320, [523, 748, 1027, 2352]], [-374976, [325, 1189, 1300, 1728]], [-373737, [391, 958, 1291, 4107]], [-371712, [331, 1123, 1452, 1456]], [-370440, [388, 955, 1323, 1363]], [-370440, [523, 712, 1147, 1323]], [-367356, [445, 841, 1120, 1452]], [-365904, [475, 787, 1084, 3267]], [-365040, [323, 1163, 1280, 4563]], [-363825, [422, 863, 1247, 1323]], [-361152, [509, 797, 884, 1728]], [-360789, [575, 731, 818, 2523]], [-355488, [587, 656, 899, 1587]], [-349920, [592, 667, 835, 2187]], [-349809, [566, 623, 1083, 1295]], [-345477, [394, 907, 1083, 1519]], [-343077, [551, 626, 1091, 2883]], [-341040, [337, 1012, 1345, 2352]], [-338997, [538, 691, 867, 1591]], [-338985, [302, 1127, 1355, 2187]], [-334425, [391, 859, 1174, 3675]], [-333564, [320, 1049, 1277, 4332]], [-331545, [478, 703, 1315, 2883]], [-330096, [355, 976, 1075, 1587]], [-330000, [419, 851, 944, 1875]], [-329280, [572, 647, 815, 2352]], [-328560, [323, 1052, 1163, 4107]], [-328125, [367, 943, 1042, 1875]], [-323817, [446, 731, 1083, 1271]], [-322896, [475, 700, 979, 2883]], [-322161, [311, 1070, 1175, 1587]], [-320892, [521, 653, 896, 1452]], [-317400, [443, 788, 875, 1587]], [-315900, [433, 757, 972, 1408]], [-312741, [575, 650, 731, 2187]], [-310365, [527, 602, 1295, 3267]], [-305184, [499, 652, 867, 1435]], [-303240, [355, 868, 1083, 1363]], [-303240, [472, 643, 1083, 1147]], [-300000, [523, 667, 748, 1875]], [-299376, [455, 671, 972, 1280]], [-297825, [383, 782, 1083, 1247]], [-297297, [391, 766, 1063, 3267]], [-296769, [487, 694, 775, 1587]], [-296352, [524, 587, 899, 1323]], [-294780, [448, 673, 1285, 3468]], [-294000, [323, 947, 1052, 3675]], [-290625, [263, 1127, 1238, 1875]], [-290145, [415, 703, 1198, 2523]], [-282576, [475, 619, 880, 2523]], [-280041, [515, 566, 867, 1295]], [-279552, [439, 727, 768, 1564]], [-278208, [353, 836, 929, 1728]], [-277725, [223, 1258, 1375, 1587]], [-276573, [367, 826, 867, 1519]], [-276480, [403, 748, 835, 1728]], [-275184, [316, 883, 1075, 1323]], [-269724, [433, 640, 901, 2028]], [-268800, [299, 899, 1196, 1200]], [-268569, [278, 971, 1175, 1323]], [-267501, [439, 610, 1015, 1083]], [-267036, [320, 845, 1049, 3468]], [-264000, [367, 727, 988, 1200]], [-263925, [499, 634, 675, 1591]], [-262392, [347, 779, 1304, 2523]], [-262353, [391, 679, 958, 2883]], [-261360, [323, 848, 947, 3267]], [-260253, [482, 551, 887, 2187]], [-259584, [491, 560, 803, 2028]], [-259233, [407, 662, 867, 1271]], [-255000, [211, 1219, 1336, 1875]], [-253704, [451, 595, 1288, 2883]], [-253500, [317, 800, 1097, 2028]], [-252720, [308, 833, 1265, 3888]], [-252720, [335, 767, 972, 1232]], [-251505, [358, 703, 1087, 2187]], [-250800, [401, 641, 884, 1200]], [-250560, [253, 1012, 1117, 1728]], [-248832, [283, 931, 972, 1456]], [-247401, [430, 619, 775, 1323]], [-245916, [361, 685, 972, 1120]], [-245760, [467, 563, 768, 1292]], [-244944, [475, 544, 787, 2187]], [-242760, [328, 787, 867, 1363]], [-242760, [427, 580, 867, 1147]], [-242592, [467, 524, 899, 1083]], [-241920, [503, 572, 647, 1728]], [-239685, [458, 527, 1067, 2523]], [-238425, [350, 707, 867, 1247]], [-232848, [323, 764, 851, 1323]], [-231525, [202, 1147, 1323, 1375]], [-231525, [283, 850, 943, 1323]], [-230640, [323, 755, 848, 2883]], [-229593, [391, 598, 859, 2523]], [-229500, [448, 517, 1057, 2700]], [-227448, [296, 779, 1187, 2187]], [-227136, [259, 880, 1195, 2028]], [-225885, [247, 922, 1255, 4107]], [-225264, [283, 796, 1075, 1083]], [-223125, [419, 551, 794, 1875]], [-222024, [388, 595, 1171, 2523]], [-221184, [203, 1100, 1211, 1728]], [-219849, [251, 878, 1083, 1175]], [-216600, [347, 632, 875, 1083]], [-216000, [443, 512, 1163, 2700]], [-215625, [307, 703, 982, 1875]], [-215325, [346, 675, 751, 1519]], [-214812, [413, 521, 896, 972]], [-214149, [394, 547, 867, 1015]], [-211680, [403, 592, 667, 1323]], [-207765, [395, 527, 962, 2187]], [-205800, [299, 731, 1256, 3675]], [-202521, [379, 550, 775, 1083]], [-202125, [247, 823, 1138, 3675]], [-201840, [323, 668, 755, 2523]], [-201825, [374, 599, 675, 1271]], [-199680, [308, 653, 1037, 3072]], [-199017, [391, 523, 766, 2187]], [-198237, [466, 507, 583, 1591]], [-196608, [364, 571, 1147, 3072]], [-195000, [251, 779, 1076, 1875]], [-194208, [416, 467, 867, 899]], [-193200, [269, 749, 836, 1200]], [-193116, [325, 640, 721, 1452]], [-192456, [331, 595, 1060, 2187]], [-192000, [307, 667, 748, 1200]], [-191100, [373, 588, 625, 1408]], [-190608, [284, 683, 851, 1083]], [-189525, [187, 1042, 1083, 1375]], [-189525, [250, 763, 943, 1083]], [-189189, [443, 506, 575, 1323]], [-189000, [307, 675, 712, 1363]], [-189000, [388, 523, 675, 1147]], [-188853, [362, 551, 707, 1587]], [-185856, [371, 560, 635, 1452]], [-185625, [323, 638, 675, 1247]], [-182952, [299, 644, 1139, 3267]], [-182505, [262, 703, 883, 1587]], [-181500, [233, 800, 893, 1452]], [-181104, [383, 551, 588, 1280]], [-180336, [256, 715, 867, 1075]], [-179928, [163, 1108, 1219, 1323]], [-179685, [247, 730, 1027, 3267]], [-178464, [427, 507, 544, 1435]], [-178125, [338, 527, 863, 1875]], [-177744, [412, 475, 619, 1587]], [-176001, [230, 791, 867, 1175]], [-174960, [323, 587, 668, 2187]], [-174000, [193, 913, 1012, 1200]], [-173400, [308, 563, 867, 875]], [-173280, [352, 523, 667, 1083]], [-172380, [385, 448, 853, 2028]], [-172032, [251, 731, 768, 1196]], [-170625, [391, 454, 679, 1875]], [-168960, [295, 583, 768, 988]], [-168000, [383, 503, 572, 1200]], [-167865, [182, 923, 1083, 1127]], [-166656, [229, 768, 805, 1300]], [-165048, [212, 779, 971, 1587]], [-164280, [187, 907, 1240, 4107]], [-163761, [431, 470, 507, 1295]], [-162240, [323, 512, 947, 2028]], [-162129, [334, 487, 775, 867]], [-161733, [331, 507, 682, 1519]], [-161448, [299, 563, 1028, 2883]], [-160512, [317, 509, 768, 884]], [-158565, [247, 643, 922, 2883]], [-157437, [311, 551, 626, 1323]], [-157248, [391, 432, 607, 1564]], [-156156, [320, 509, 665, 2028]], [-154869, [386, 443, 575, 1083]], [-152592, [251, 608, 851, 867]], [-152145, [223, 703, 790, 1323]], [-151725, [178, 867, 943, 1375]], [-151725, [223, 682, 867, 943]], [-151593, [347, 507, 542, 1271]], [-151200, [371, 416, 675, 899]], [-150765, [287, 527, 770, 1587]], [-150000, [323, 512, 587, 1875]], [-148176, [355, 475, 544, 1323]], [-147288, [148, 1003, 1083, 1219]], [-147000, [187, 808, 1123, 3675]], [-143745, [143, 1007, 1118, 4107]], [-141960, [292, 507, 643, 1363]], [-141960, [355, 472, 507, 1147]], [-141933, [363, 439, 538, 1591]], [-141288, [299, 488, 923, 2523]], [-139656, [235, 595, 856, 1587]], [-139425, [302, 507, 575, 1247]], [-138765, [247, 562, 823, 2523]], [-138720, [307, 460, 667, 867]], [-138240, [395, 432, 467, 1292]], [-137592, [179, 779, 872, 1323]], [-134385, [167, 830, 867, 1127]], [-129276, [241, 565, 640, 972]], [-128625, [143, 902, 1007, 3675]], [-127776, [363, 400, 499, 1435]], [-126960, [323, 443, 512, 1587]], [-125685, [242, 527, 683, 1323]], [-125229, [322, 439, 507, 1015]], [-124416, [140, 899, 1115, 3888]], [-124416, [275, 491, 560, 972]], [-123981, [335, 386, 575, 867]], [-123648, [209, 593, 768, 836]], [-123420, [277, 448, 673, 1452]], [-122880, [235, 523, 748, 768]], [-122472, [203, 731, 1256, 2187]], [-122472, [299, 419, 824, 2187]], [-121500, [173, 713, 800, 972]], [-120393, [334, 391, 523, 1323]], [-120285, [247, 487, 730, 2187]], [-120000, [139, 931, 1264, 1875]], [-118800, [224, 539, 675, 851]], [-118125, [202, 607, 675, 943]], [-117912, [139, 867, 904, 1219]], [-117249, [363, 398, 431, 1295]], [-116160, [227, 512, 755, 1452]], [-115797, [322, 363, 619, 1519]], [-115320, [187, 628, 907, 2883]], [-113568, [332, 371, 507, 899]], [-112320, [308, 365, 653, 1728]], [-111804, [320, 377, 509, 1452]], [-111360, [157, 733, 768, 1012]], [-110592, [307, 364, 739, 1728]], [-108864, [139, 787, 880, 972]], [-108537, [326, 363, 491, 1271]], [-108000, [268, 403, 667, 675]], [-107520, [287, 383, 572, 768]], [-105840, [323, 380, 443, 1323]], [-105456, [199, 640, 1135, 2028]], [-105456, [220, 507, 571, 1075]], [-105000, [164, 731, 1139, 1875]], [-105000, [299, 356, 731, 1875]], [-104625, [158, 675, 743, 1127]], [-103173, [227, 482, 551, 867]], [-103125, [247, 418, 643, 1875]], [-102921, [206, 507, 635, 1175]], [-102885, [203, 527, 602, 1083]], [-101640, [283, 363, 580, 1363]], [-101640, [328, 363, 427, 1147]], [-101568, [112, 931, 1147, 1587]], [-101400, [248, 443, 507, 875]], [-100920, [187, 547, 808, 2523]], [-100920, [340, 403, 1123, 2523]], [-100905, [143, 710, 803, 2883]], [-99825, [287, 363, 518, 1247]], [-99705, [163, 622, 703, 867]], [-98736, [95, 1040, 1151, 1452]], [-98553, [283, 391, 454, 1083]], [-98304, [131, 768, 803, 1100]], [-98304, [140, 707, 899, 3072]], [-97500, [300, 337, 517, 1408]], [-97104, [259, 412, 475, 867]], [-96768, [227, 432, 587, 1196]], [-95304, [163, 595, 676, 1083]], [-95040, [247, 432, 463, 988]], [-95013, [243, 418, 499, 1591]], [-94809, [262, 379, 507, 775]], [-92256, [275, 464, 1115, 2883]], [-91200, [79, 1159, 1200, 1276]], [-90288, [257, 401, 432, 884]], [-90168, [131, 692, 779, 867]], [-89661, [295, 363, 394, 1015]], [-89232, [203, 476, 507, 851]], [-88872, [131, 731, 1028, 1587]], [-88725, [187, 507, 538, 943]], [-88305, [143, 623, 710, 2523]], [-87480, [187, 472, 715, 2187]], [-87480, [283, 403, 1012, 2187]], [-87285, [247, 355, 562, 1587]], [-86016, [220, 535, 1111, 3072]], [-85536, [243, 379, 460, 1435]], [-82620, [193, 448, 517, 972]], [-81312, [299, 332, 363, 899]], [-81120, [235, 352, 507, 667]], [-80736, [275, 395, 1004, 2523]], [-80325, [194, 419, 551, 675]], [-78489, [243, 371, 398, 1295]], [-78204, [181, 433, 588, 640]], [-78000, [257, 308, 497, 1200]], [-78000, [263, 300, 503, 1232]], [-77760, [155, 512, 587, 972]], [-77625, [142, 547, 675, 703]], [-76800, [211, 364, 571, 1200]], [-76545, [143, 542, 623, 2187]], [-76032, [191, 476, 911, 1728]], [-75504, [127, 640, 919, 1452]], [-75504, [211, 363, 508, 1075]], [-75000, [187, 403, 628, 1875]], [-75000, [232, 403, 907, 1875]], [-74844, [269, 320, 377, 972]], [-74088, [104, 731, 923, 1323]], [-74088, [248, 299, 563, 1323]], [-73500, [137, 557, 588, 800]], [-72765, [247, 298, 487, 1323]], [-72657, [243, 311, 446, 1271]], [-72600, [227, 363, 392, 875]], [-72501, [251, 290, 507, 575]], [-70200, [116, 611, 675, 779]], [-69984, [275, 332, 899, 2187]], [-69888, [192, 367, 511, 1564]], [-69552, [173, 432, 461, 836]], [-69360, [128, 695, 1103, 3468]], [-69120, [187, 403, 432, 748]], [-68040, [243, 307, 388, 1147]], [-67881, [235, 334, 363, 775]], [-66825, [243, 278, 467, 1247]], [-66300, [269, 300, 329, 896]], [-66096, [71, 935, 972, 1040]], [-65856, [115, 588, 619, 880]], [-65856, [220, 391, 895, 2352]], [-65712, [91, 883, 1216, 4107]], [-65625, [143, 467, 542, 1875]], [-64125, [143, 458, 527, 675]], [-63888, [188, 363, 419, 851]], [-63525, [178, 363, 475, 943]], [-63480, [187, 340, 547, 1587]], [-63480, [187, 403, 808, 1587]], [-61440, [192, 347, 395, 1292]], [-61425, [199, 334, 391, 675]], [-60648, [83, 731, 824, 1083]], [-60648, [203, 299, 488, 1083]], [-60480, [215, 287, 432, 572]], [-60333, [167, 362, 507, 551]], [-60021, [243, 274, 355, 1015]], [-58812, [137, 704, 1229, 2028]], [-58305, [127, 478, 507, 703]], [-58125, [106, 799, 1231, 1875]], [-58080, [208, 307, 363, 667]], [-58029, [266, 455, 1223, 2523]], [-57477, [147, 403, 466, 1591]], [-56784, [187, 304, 475, 507]], [-55545, [62, 1007, 1235, 1587]], [-55545, [143, 398, 467, 1587]], [-55488, [67, 832, 867, 931]], [-55296, [140, 395, 539, 1728]], [-54777, [319, 382, 1219, 2883]], [-54432, [243, 272, 299, 899]], [-54000, [128, 527, 887, 2700]], [-54000, [227, 272, 323, 675]], [-53724, [49, 1120, 1237, 1452]], [-52920, [148, 403, 715, 1323]], [-52920, [187, 283, 472, 1323]], [-52800, [119, 476, 719, 1200]], [-52728, [107, 507, 536, 779]], [-52272, [91, 691, 988, 3267]], [-52224, [260, 449, 1217, 3072]], [-51909, [218, 251, 363, 575]], [-50784, [224, 275, 707, 1587]], [-50544, [79, 640, 727, 972]], [-50301, [215, 455, 1106, 2187]], [-49920, [173, 308, 365, 768]], [-49197, [79, 799, 1114, 1587]], [-49152, [139, 364, 427, 768]], [-48600, [212, 243, 347, 875]], [-48552, [164, 299, 419, 867]], [-48384, [220, 271, 703, 1728]], [-48165, [122, 395, 507, 527]], [-47685, [202, 247, 355, 867]], [-47040, [107, 443, 512, 588]], [-46305, [47, 1007, 1118, 1323]], [-46305, [143, 335, 398, 1323]], [-46137, [166, 283, 391, 507]], [-46128, [91, 604, 883, 2883]], [-45441, [214, 243, 295, 775]], [-45276, [185, 269, 320, 588]], [-45084, [160, 601, 1213, 3468]], [-44616, [100, 451, 507, 595]], [-43953, [147, 302, 407, 1271]], [-43320, [115, 403, 628, 1083]], [-43320, [187, 232, 403, 1083]], [-43200, [133, 532, 997, 1728]], [-43197, [146, 311, 363, 551]], [-42768, [179, 243, 368, 851]], [-42336, [179, 275, 620, 1323]], [-42240, [192, 223, 367, 988]], [-41745, [118, 363, 415, 703]], [-41553, [262, 319, 991, 2187]], [-41160, [147, 292, 355, 1147]], [-41013, [58, 799, 1003, 1323]], [-40656, [160, 259, 363, 475]], [-40560, [128, 383, 695, 2028]], [-40560, [188, 227, 323, 507]], [-40368, [91, 523, 784, 2523]], [-40128, [192, 221, 317, 884]], [-39984, [260, 317, 989, 2352]], [-38880, [187, 243, 268, 667]], [-37905, [143, 278, 335, 1083]], [-37800, [59, 644, 675, 731]], [-37800, [131, 299, 356, 675]], [-37125, [163, 247, 298, 675]], [-36504, [35, 1091, 1208, 4563]], [-36501, [131, 455, 890, 1587]], [-35937, [119, 599, 1094, 3267]], [-35625, [211, 319, 886, 1875]], [-34992, [91, 448, 691, 2187]], [-34749, [191, 218, 243, 575]], [-34680, [88, 403, 547, 867]], [-34656, [140, 275, 539, 1083]], [-34485, [107, 338, 363, 527]], [-33792, [71, 476, 551, 768]], [-33573, [43, 799, 898, 1083]], [-33264, [108, 311, 383, 1280]], [-33033, [139, 238, 363, 391]], [-32928, [147, 251, 272, 899]], [-32856, [35, 980, 1091, 4107]], [-31944, [91, 363, 388, 595]], [-31713, [119, 518, 983, 2883]], [-30720, [163, 192, 307, 748]], [-30576, [55, 559, 588, 640]], [-30345, [143, 227, 278, 867]], [-30153, [166, 319, 787, 1587]], [-30000, [73, 532, 793, 1200]], [-30000, [91, 379, 604, 1875]], [-29376, [209, 260, 785, 1728]], [-29325, [75, 394, 439, 1591]], [-29040, [128, 263, 527, 1452]], [-29040, [155, 188, 323, 363]], [-28917, [131, 243, 266, 551]], [-28749, [55, 874, 1207, 4107]], [-28188, [41, 704, 797, 972]], [-28080, [113, 257, 308, 432]], [-27753, [119, 443, 878, 2523]], [-27744, [107, 275, 464, 867]], [-27648, [91, 307, 364, 432]], [-27489, [147, 199, 262, 775]], [-27216, [139, 220, 243, 475]], [-27000, [67, 403, 472, 675]], [-27000, [148, 187, 283, 675]], [-26880, [167, 192, 215, 572]], [-26364, [160, 313, 781, 2028]], [-26136, [35, 776, 875, 3267]], [-25500, [97, 277, 300, 448]], [-25392, [91, 316, 523, 1587]], [-25137, [127, 319, 694, 1323]], [-24909, [71, 455, 698, 1083]], [-24576, [140, 179, 275, 768]], [-24057, [119, 374, 779, 2187]], [-24000, [83, 300, 323, 512]], [-23868, [108, 233, 269, 896]], [-23625, [143, 182, 227, 675]], [-23520, [147, 172, 235, 667]], [-23085, [98, 243, 287, 527]], [-23064, [35, 683, 776, 2883]], [-22113, [118, 199, 243, 391]], [-21660, [32, 977, 1205, 4332]], [-21504, [103, 220, 391, 768]], [-21021, [147, 170, 191, 575]], [-21000, [75, 283, 328, 1147]], [-20625, [119, 311, 686, 1875]], [-20577, [94, 319, 607, 1083]], [-20328, [83, 248, 299, 363]], [-20280, [115, 187, 232, 507]], [-20184, [35, 596, 683, 2523]], [-20181, [55, 595, 874, 2883]], [-19965, [103, 202, 247, 363]], [-19941, [50, 455, 611, 867]], [-19440, [128, 155, 243, 323]], [-19440, [128, 167, 383, 972]], [-19200, [37, 532, 613, 768]], [-19008, [47, 407, 432, 476]], [-18876, [160, 205, 601, 1452]], [-17661, [55, 514, 775, 2523]], [-17496, [35, 515, 596, 2187]], [-17493, [122, 147, 227, 551]], [-17457, [119, 254, 599, 1587]], [-17340, [32, 773, 977, 3468]], [-17328, [91, 208, 379, 1083]], [-16800, [75, 236, 251, 899]], [-16473, [67, 319, 526, 867]], [-16464, [124, 147, 187, 475]], [-16224, [59, 275, 332, 507]], [-15360, [48, 323, 347, 1292]], [-15309, [55, 439, 682, 2187]], [-14520, [43, 340, 363, 403]], [-13872, [91, 163, 316, 867]], [-13824, [107, 140, 179, 432]], [-13824, [108, 131, 203, 560]], [-13608, [68, 203, 243, 299]], [-13500, [32, 593, 773, 2700]], [-13377, [103, 147, 166, 391]], [-13365, [82, 163, 243, 247]], [-13056, [65, 260, 449, 768]], [-12825, [46, 319, 451, 675]], [-12696, [35, 371, 440, 1587]], [-12636, [121, 160, 445, 972]], [-12480, [77, 173, 192, 308]], [-12288, [67, 192, 211, 364]], [-12096, [55, 220, 271, 432]], [-12000, [75, 163, 208, 667]], [-11913, [119, 158, 443, 1083]], [-11760, [95, 128, 263, 588]], [-11760, [107, 128, 147, 323]], [-11109, [55, 307, 514, 1587]], [-10800, [91, 124, 259, 675]], [-10140, [32, 437, 593, 2028]], [-9720, [67, 148, 187, 243]], [-9633, [31, 319, 382, 507]], [-9261, [55, 250, 439, 1323]], [-8721, [27, 326, 335, 1295]], [-8664, [35, 251, 308, 1083]], [-8505, [83, 110, 143, 243]], [-8316, [89, 108, 125, 320]], [-8232, [59, 147, 164, 299]], [-8085, [67, 130, 147, 247]], [-7776, [35, 224, 243, 275]], [-7644, [61, 160, 313, 588]], [-7581, [55, 199, 370, 1083]], [-7425, [86, 119, 311, 675]], [-7344, [29, 260, 317, 432]], [-7260, [32, 305, 437, 1452]], [-6936, [35, 200, 251, 867]], [-6825, [75, 94, 139, 391]], [-6720, [48, 143, 167, 572]], [-6144, [59, 107, 140, 192]], [-6069, [55, 154, 307, 867]], [-6048, [27, 227, 236, 899]], [-6000, [47, 128, 167, 300]], [-6000, [75, 92, 107, 323]], [-5880, [52, 115, 147, 187]], [-5808, [64, 91, 163, 363]], [-5577, [59, 119, 254, 507]], [-5376, [31, 175, 192, 220]], [-5145, [62, 83, 143, 147]], [-4860, [32, 197, 305, 972]], [-4125, [58, 75, 103, 247]], [-4056, [35, 116, 155, 507]], [-3993, [38, 119, 203, 363]], [-3888, [43, 91, 124, 243]], [-3861, [27, 146, 155, 575]], [-3549, [55, 82, 199, 507]], [-3000, [43, 75, 88, 187]], [-2940, [32, 113, 197, 588]], [-2904, [35, 83, 116, 363]], [-2673, [23, 119, 158, 243]], [-2625, [47, 62, 75, 143]], [-2160, [23, 95, 108, 128]], [-2160, [27, 83, 92, 323]], [-1944, [35, 56, 83, 243]], [-1701, [34, 55, 115, 243]], [-1536, [35, 48, 59, 140]], [-1500, [32, 53, 113, 300]], [-1200, [19, 64, 75, 91]], [-1029, [19, 55, 82, 147]], [-945, [27, 38, 47, 143]], [-540, [17, 32, 53, 108]], [-216, [11, 20, 27, 35]], [1215, [7, 22, 103, 243]], [1344, [5, 20, 101, 192]], [1815, [7, 43, 142, 363]], [2535, [7, 70, 187, 507]], [3024, [20, 41, 185, 432]], [3300, [1, 64, 181, 300]], [3375, [7, 103, 238, 675]], [4335, [7, 142, 295, 867]], [5376, [20, 101, 293, 768]], [5415, [7, 187, 358, 1083]], [6468, [37, 64, 289, 588]], [6591, [14, 95, 287, 507]], [7935, [7, 295, 502, 1587]], [8112, [11, 32, 227, 507]], [8640, [7, 28, 223, 432]], [9375, [7, 358, 583, 1875]], [10692, [64, 97, 421, 972]], [10800, [11, 59, 284, 675]], [10935, [7, 427, 670, 2187]], [11271, [62, 95, 419, 867]], [12096, [20, 293, 581, 1728]], [12615, [7, 502, 763, 2523]], [13872, [11, 92, 347, 867]], [14415, [7, 583, 862, 2883]], [14739, [31, 175, 490, 867]], [15360, [28, 55, 343, 768]], [15972, [64, 181, 577, 1452]], [16335, [7, 670, 967, 3267]], [16464, [20, 425, 761, 2352]], [17199, [95, 134, 575, 1323]], [17328, [11, 131, 416, 1083]], [18411, [58, 175, 571, 1083]], [18468, [29, 224, 569, 972]], [20535, [7, 862, 1195, 4107]], [20631, [95, 179, 662, 1587]], [21168, [11, 176, 491, 1323]], [21504, [20, 581, 965, 3072]], [22308, [64, 289, 757, 2028]], [24000, [28, 127, 487, 1200]], [25392, [11, 227, 572, 1587]], [26979, [130, 175, 751, 1587]], [27075, [2, 407, 743, 1083]], [27216, [20, 761, 1193, 3888]], [27216, [47, 80, 479, 972]], [27588, [89, 224, 749, 1452]], [27744, [16, 115, 475, 867]], [28431, [95, 287, 854, 2187]], [29700, [64, 421, 961, 2700]], [30000, [11, 284, 659, 1875]], [32799, [95, 350, 959, 2523]], [33075, [23, 407, 842, 1323]], [34560, [28, 223, 655, 1728]], [34656, [43, 115, 556, 1083]], [34992, [11, 347, 752, 2187]], [37179, [175, 226, 955, 2187]], [37479, [95, 419, 1070, 2883]], [38148, [64, 577, 1189, 3468]], [38532, [173, 224, 953, 2028]], [39675, [50, 407, 947, 1587]], [39744, [85, 340, 949, 1728]], [40368, [11, 416, 851, 2523]], [40656, [80, 119, 647, 1452]], [42336, [76, 115, 643, 1323]], [42471, [95, 494, 1187, 3267]], [42891, [175, 283, 1066, 2523]], [43320, [8, 203, 635, 1083]], [46023, [19, 559, 1054, 1587]], [46128, [11, 491, 956, 2883]], [46875, [83, 407, 1058, 1875]], [49011, [175, 346, 1183, 2883]], [51300, [224, 281, 1181, 2700]], [53568, [17, 644, 1169, 1728]], [54096, [169, 340, 1177, 2352]], [54375, [46, 559, 1171, 1875]], [54675, [122, 407, 1175, 2187]], [56784, [80, 215, 839, 2028]], [58800, [11, 659, 1184, 3675]], [61440, [28, 487, 1063, 3072]], [63480, [68, 203, 827, 1587]], [63888, [31, 256, 823, 1452]], [69984, [115, 211, 940, 2187]], [74088, [19, 52, 619, 1323]], [75000, [107, 203, 932, 1875]], [76800, [11, 44, 611, 1200]], [80736, [115, 268, 1051, 2523]], [87480, [152, 203, 1043, 2187]], [88872, [19, 91, 712, 1587]], [89232, [103, 256, 1039, 2028]], [89856, [23, 380, 1031, 1728]], [92256, [115, 331, 1168, 2883]], [105000, [19, 136, 811, 1875]], [105000, [19, 451, 1144, 1875]], [110592, [44, 83, 803, 1728]], [122472, [19, 187, 916, 2187]], [141288, [19, 244, 1027, 2523]], [150528, [44, 179, 1019, 2352]], [159375, [23, 62, 887, 1875]], [161448, [19, 307, 1144, 2883]], [162240, [67, 112, 1003, 2028]], [164160, [13, 52, 877, 1728]], [185895, [23, 107, 998, 2187]], [192456, [59, 155, 1112, 2187]], [214455, [23, 158, 1115, 2523]], [223440, [52, 97, 1105, 2352]]]

これより、例えば、
7 × 22 + 1215 = 37^2,

7 × 103 + 1215 = 44^2,

7 × 243 + 1215 = 54^2,

22 × 103 + 1215 = 59^2,

22 × 243 + 1215 = 81^2,

103 × 243 + 1215 = 162^2

が見つかったことになる。