Solutions of Diophantine equation x/y+y/z+z/x=n (1 <= n <= 100) When (x,y,z) is a solution of the equation and l=lcm(x,y,z), then (l/z,l/y,l/x) also becomes the solution. n | (x, y, z) | lcm(x,y,z) | ---+-----------+---+------------------------------------------------------------ 3 | (1, 1, 1) | 1 | 5 | (1, 2, 4) | 4 | 6 | (2, 12, 9) | 36 | 6 | (3, 18, 4) | 36 | derived from (2, 12, 9) 9 | (12, 63, 98) | 1764 | 9 | (18, 28, 147) | 1764 | derived from (12, 63, 98) ---+---------------------------------------------------------------------------- 10 | (175, 882, 1620) | 396900 | 10 | (245, 450, 2268) | 396900 | derived from (175, 882, 1620) 13 | (1053, 6422, 12996) | 19766916 | 13 | (1521, 3078, 18772) | 19766916 | derived from (1053, 6422, 12996) 14 | (28, 637, 338) | 33124 | 14 | (52, 1183, 98) | 33124 | derived from (28, 637, 338) 15 | (3, -63, 49) | 441 | 15 | (-7, 147, 9) | 441 | derived from (3, -63, 49) 16 | (2511, -67270, 44100) | 381420900 | 16 | (-5670, 151900, 8649) | 381420900 | derived from (2511, -67270, 44100) 17 | (450, 11988, 6845) | 11088900 | 17 | (925, 24642, 1620) | 11088900 | derived from (450, 11988, 6845) 18 | (7098, 167580, 117325) | 2690496900 | 18 | (16055, 379050, 22932) | 2690496900 | derived from (7098, 167580, 117325) 19 | (5, 225, 81) | 2025 | 19 | (9, 405, 25) | 2025 | derived from (5, 225, 81) ---+---------------------------------------------------------------------------- 20 | (2366, -11956, 48373) | 123254404 | 20 | (2548, -10309, 52094) | 123254404 | derived from (2366, -11956, 48373) 21 | (52, 3549, 882) | 298116 | 21 | (84, 5733, 338) | 298116 | derived from (52, 3549, 882) 26 | (3078, 131404, 74529) | 968578884 | 26 | (7371, 314678, 12996) | 968578884 | derived from (3078, 131404, 74529) 29 | (31347, 336518, 894348) | 44648535204 | 29 | (49923, 132678, 1424332) | 44648535204 | derived from (31347, 336518, 894348) ---+---------------------------------------------------------------------------- 30 | (84, 13671, 1922) | 1695204 | 30 | (124, 20181, 882) | 1695204 | derived from (84, 13671, 1922) 31 | (27, -26973, 1369) | 998001 | 31 | (-37, 36963, 729) | 998001 | derived from (27, -26973, 1369) 35 | (3724, -35017, 131726) | 665743204 | 35 | (5054, -19012, 178771) | 665743204 | derived from (3724, -35017, 131726) 36 | (3822, -918684, 159607) | 6797342916 | 36 | (-7399, 1778478, 42588) | 6797342916 | derived from (3822, -918684, 159607) 38 | (739900, 14341829, 27694870) | 44202951160900 | 38 | (1596070, 3082100, 59741791) | 44202951160900 | derived from (739900, 14341829, 27694870) ---+---------------------------------------------------------------------------- 40 | (2, -36, 81) | 324 | 40 | (4, -9, 162) | 324 | derived from (2, -36, 81) 41 | (2, 36, 81) | 324 | 41 | (4, 9, 162) | 324 | derived from (2, 36, 81) 41 | (4, -208, 169) | 2704 | 41 | (-13, 676, 16) | 2704 | derived from (4, -208, 169) 41 | (5, 350, 196) | 4900 | 41 | (14, 980, 25) | 4900 | derived from (5, 350, 196) 44 | (199994, -251364204, 12744459) | 74318089190436 | 44 | (-295659, 371601594, 5831404) | 74318089190436 | derived from (199994, -251364204, 12744459) 47 | (529948, -113812205, 27132950) | 138871376296900 | 47 | (-1220180, 262047175, 5118182) | 138871376296900 | derived from (529948, -113812205, 27132950) ---+---------------------------------------------------------------------------- 51 | (1053, 13013, 53361) | 81162081 | 51 | (1521, 6237, 77077) | 81162081 | derived from (1521, 6237, 77077) 53 | (28, 1323, 1458) | 142884 | 53 | (98, 108, 5103) | 142884 | derived from (28, 1323, 1458) 54 | (172, 105393, 6498) | 24029604 | 54 | (228, 139707, 3698) | 24029604 | derived from (172, 105393, 6498) 57 | (32851, 2567110, 1825900) | 287285280100 | 57 | (111910, 8745100, 157339) | 287285280100 | derived from (32851, 2567110, 1825900) ---+---------------------------------------------------------------------------- 62 | (4467832378776170000, -51609086900999886977, 278221158496143039700) | 1602539713289999534454631142553484090000 | 62 | (5759949106502679700, -31051502933274170000, 358683938301411320777) | 1602539713289999534454631142553484090000 | derived from (4467832378776170000, -51609086900999886977, 278221158496143039700) 63 | (55091127, -3078168975, 3519904375) | 708929941509050625 | 63 | (201406023, -230308975, 12868314375) | 708929941509050625 | derived from (55091127, -3078168975, 3519904375) 64 | (3322360264652576, -72476281617030144, 213909032364083559) | 1384356148672642887479494209094656 | 64 | (6471704973712384, -19100816402084199, 416678517197895456) | 1384356148672642887479494209094656 | derived from (3322360264652576, -72476281617030144, 213909032364083559) 66 | (3, 126, 196) | 1764 | 66 | (9, 14, 588) | 1764 | derived from (3, 126, 196) 67 | (9659759725, 1331664823125, 626604844437) | 40200982439861193575625 | 67 | (30188514213, 4161695899725, 64156833125) | 40200982439861193575625 | derived from (30188514213, 4161695899725, 64156833125) 69 | (167580, 4720075, 11488218) | 4354609032900 | 69 | (379050, 922572, 25985255) | 4354609032900 | derived from (379050, 922572, 25985255) 69 | (429100464, -5846691951, 29723828836) | 17716691881532167056 | 69 | (596043396, -3030207856, 41287981179) | 17716691881532167056 | derived from (429100464, -5846691951, 29723828836) ---+---------------------------------------------------------------------------- 70 | (657696015121852, -1189119085505749296, 59240782273149603) | 1289973820680844369745272253960976 | 70 | (-1084814663564331, 1961352647760606588, 21775097680732592) | 1289973820680844369745272253960976 | derived from (657696015121852, -1189119085505749296, 59240782273149603) 71 | (441, -5427, 31423) | 17816841 | 71 | (567, -3283, 40401) | 17816841 | derived from (441, -5427, 31423) 74 | (44257878, 28839838428, 2822851717) | 2350251384296973444 | 74 | (81493223, 53103571398, 832580532) | 2350251384296973444 | derived from (81493223, 53103571398, 832580532) 76 | (140733684, -25465550877, 11021701754) | 11598447413419838244 | 76 | (-455456372, 82414153341, 1052328186) | 11598447413419838244 | derived from (140733684, -25465550877, 11021701754) 76 | (3867000084, -71907044976, 295042421167) | 1888078547166714259344 | 76 | (6399346032, -26257212319, 488254074516) | 1888078547166714259344 | derived from (3867000084, -71907044976, 295042421167) 77 | (175, -2548, 13520) | 3312400 | 77 | (245, -1300, 18928) | 3312400 | derived from (175, -2548, 13520) 77 | (2828070, 699734700, 208247323) | 5537775287412900 | 77 | (7914107, 1958146470, 26592300) | 5537775287412900 | derived from (2828070, 699734700, 208247323) ---+---------------------------------------------------------------------------- 83 | (225, 4941, 18605) | 7535025 | 83 | (405, 1525, 33489) | 7535025 | derived from (225, 4941, 18605) 84 | (31, -53816, 3136) | 3013696 | 84 | (-56, 97216, 961) | 3013696 | derived from (31, -53816, 3136) 86 | (292, 484939, 16562) | 176517796 | 86 | (364, 604513, 10658) | 176517796 | derived from (292, 484939, 16562) 87 | (5, -525, 441) | 11025 | 87 | (-21, 2205, 25) | 11025 | derived from (5, -525, 441) ---+---------------------------------------------------------------------------- 94 | (269306, 525907620, 16967475) | 179410755024900 | 94 | (341145, 666196650, 10573804) | 179410755024900 | derived from (269306, 525907620, 16967475) 94 | (73329944471, -6426538133976, 6961545912384) | 2207883181046165290737216 | 94 | (317154150649, -343557158616, 30108889308096) | 2207883181046165290737216 | derived from (73329944471, -6426538133976, 6961545912384) 96 | (45, -950, 4332) | 324900 | 96 | (75, -342, 7220) | 324900 | derived from (45, -950, 4332) 98 | (92700700341746741712, -12016141901847657310464, 9206376534947615098369) | 4720172437487373689440793182623596214683904 | 98 | (-392819298910041852961, 50918411836007412579792, 512706863505907190016) | 4720172437487373689440793182623596214683904 | derived from (92700700341746741712, -12016141901847657310464, 9206376534947615098369) 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