一题 \(x^{131}+y^{137}+z^{139}=w^{149}\) 多解

ysr

蔡家雄 发表于 2025-4-10 10:46
求 \(x^2 - 13*y^2= - 237\) 的正整数解，，

x=20  y=7
x=176  y=49
x=436  y=121
x=3400  y=943
x=29360  y=8143
x=228884  y=63481
x=566104  y=157009
x=4413220  y=1224007
x=38109260  y=10569607

5.453125

ysr

蔡家雄 发表于 2025-4-10 10:48
求 \(x^2 - 29*y^2= 875\) 的正整数解，，

x=40  y=5
x=76  y=13
x=620  y=115
x=1352  y=251
x=3172  y=589
x=6920  y=1285
x=58736  y=10907
x=128140  y=23795
x=655940  y=121805
x=1431016  y=265733
x=12146320  y=2255515
x=26498732  y=4920691
x=62176192  y=11545829

5.539063

ysr

蔡家雄 发表于 2025-4-10 10:48
求 \(x^2 - 29*y^2= - 875\) 的正整数解，，

x=13  y=6
x=45  y=10
x=419  y=78
x=915  y=170
x=4685  y=870
x=10221  y=1898
x=86755  y=16110
x=189267  y=35146
x=444093  y=82466
x=968845  y=179910
x=8223459  y=1527058
x=17940515  y=3331470
x=91836285  y=17053570

5.40625

ysr

蔡家雄 发表于 2025-4-10 17:54
求 \(x^2 - 53*y^2= 2233\) 的正整数解，，

x=75  y=8
x=181  y=24
x=1515  y=208
x=2301  y=316
x=32149  y=4416
x=48835  y=6708
x=415869  y=57124
x=1110275  y=152508
x=8827075  y=1212492
x=23566269  y=3237076

5.263672

ysr

蔡家雄 发表于 2025-4-10 17:55
求 \(x^2 - 53*y^2= - 2233\) 的正整数解，，

x=82  y=13
x=130  y=19
x=1142  y=157
x=3050  y=419
x=24250  y=3331
x=64742  y=8893
x=551330  y=75731
x=837482  y=115037
x=11702318  y=1607437
x=17776070  y=2441731

5.322266

ysr

蔡家雄 发表于 2025-4-10 17:57
求 \(x^2 - 85*y^2= 4599\) 的正整数解，，

x=82  y=5
x=122  y=11
x=258  y=27
x=1578  y=171
x=6242  y=677
x=16918  y=1835
x=38842  y=4213
x=105278  y=11419
x=416622  y=45189
x=2592582  y=281205
x=5882558  y=638053
x=10259758  y=1112827
x=36606358  y=3970517
x=63845078  y=6924971

5.4375

ysr

蔡家雄 发表于 2025-4-10 17:57
求 \(x^2 - 85*y^2= - 4599\) 的正整数解，，

x=29  y=8
x=131  y=16
x=549  y=60
x=3429  y=372
x=7781  y=844
x=13571  y=1472
x=48421  y=5252
x=84451  y=9160
x=191619  y=20784
x=1192419  y=129336
x=4718821  y=511828
x=12789979  y=1387268
x=29364581  y=3185036
x=79590299  y=8632780

5.367188

Treenewbee

蔡家雄 发表于 2025-4-11 07:06
求 \(x^2 - 13*y^2= 3081\) 的正整数解，，

{{91,20},{637,176},{1573,436},{12259,3400},{105859,29360},{825253,228884},{2041117,566104},{15912091,4413220},{137404891,38109260},{1071177757,297091256},{2649368293,734802556},{20653881859,5728356160},{178351442659,49465790120},{1390387903333,385624221404},{3438878003197,953773151584},{26808722740891,7435401882460},{231500035166491,64206557466500},{1804722427348477,500539942291136},{4463660998781413,1237996815953476},{34797701463794659,9651145915076920},{300486867294662659,83340062125726880},{2342528320310419813,649700459469673124},{5793828537540270877,1606918913334460264},{45167389691282726491,12527179962367959700}}

Treenewbee

蔡家雄 发表于 2025-4-11 07:06
求 \(x^2 - 13*y^2= - 3081\) 的正整数解，，

{{26,17},{338,95},{2938,815},{22906,6353},{56654,15713},{441662,122495},{3813862,1057775},{29732014,8246177},{73536866,20395457},{573276938,158998415},{4950389938,1372991135},{38592131266,10703531393},{95450795414,26473287473},{744113023862,206379820175},{6425602325662,1782141435455},{50092556651254,13893175501937},{123895058910506,34362306744497},{965858131695938,267880847588735},{8340426868319338,2313218210229455},{65020099941196426,18033331097982833},{160815691015041374,44602247681069633},{1253683110828303662,347709133790357855},{10825867649476175062,3002555454736397135},{84396039631116309694,23407249872006215297}}

Treenewbee

蔡家雄 发表于 2025-4-11 07:53
求 \(x^2 - 29*y^2= 25375\) 的正整数解，，

{{174,13},{290,45},{2262,419},{4930,915},{25230,4685},{55042,10221},{467190,86755},{1019234,189267},{2391514,444093},{5217390,968845},{44284682,8223459},{96612630,17940515},{494553530,91836285},{1078931022,200352461},{9157858090,1700571555},{19979024694,3710011747},{46878457254,8705110973},{102271278490,18991299645},{868068334302,161196242899},{1893800768330,351669974115},{9694238269830,1800174853885},{21149205838202,3927308930301},{179512333812990,33334603534355},{391628841032554,72723650075427},{918911516701394,170637584848653},{2004721595743590,372267454672445},{17015875444703122,3159768745082739},{37122282564192030,6893434814661715},{190026458070654130,35287027394017485},{414566731761504582,76983109451407741},{3518800758244371890,653424896779855155},{7676708521941098814,1425528985068508307},{18012503503502267934,3344837929498185133},{39296552617494572690,7297186627497967245}}