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

Treenewbee

蔡家雄 发表于 2025-4-6 21:49
求 \(x^2 - 29*y^2= - (59*115)\) 的正整数解，，

{{262,51},{318,61},{494,93},{1306,243},{25434,4723},{66846,12413},{102862,19101},{123918,23011},{5259642,976691},{6336298,1176621},{9750234,1810573},{25625646,4758563},{498558574,92580003},{1310315786,243319533},{2016301242,374417741},{2429040898,451061571},{103099502222,19145096931},{124204113078,23064124781},{191124086374,35490851853},{502313911586,93277351683},{9772745142114,1814753214083},{25684809970326,4769549473453},{39523536842822,7339336539981},{47614059558678,8841708891731},{2020956437296002,375282189064771},{2434649018218658,452102972780541},{3746414331352914,695691676211933},{9846357269283126,1828422642931603},{191565349777160054,35572792409874963},{503473643728014466,93492708535306173},{774740367176695602,143865674482289821},{933330793040165258,173315177244649491},{39614787980776728982,7356281450902544211},{47723989930918021038,8862122449380039901},{73437213532055733854,13636948201615458813}}

ysr

蔡家雄 发表于 2025-4-6 23:11
求 \(x^2 - 53*y^2= (107*211)\) 的正整数解，，

x=2567  y=352
x=2945  y=404
x=254105  y=34904
x=291583  y=40052

11.57813

ysr

蔡家雄 发表于 2025-4-6 23:12
求 \(x^2 - 53*y^2= - (107*211)\) 的正整数解，，

x=690  y=97
x=794  y=111
x=933594  y=128239
x=1071290  y=147153
x=92494910  y=12705153

11.88281

ysr

蔡家雄 发表于 2025-4-6 23:14
求 \(x^2 - 85*y^2= (171*339)\) 的正整数解，，

x=327  y=24
x=353  y=28
x=1313  y=140
x=1823  y=196
x=6753  y=732
x=7527  y=816
x=44697  y=4848
x=49823  y=5404
x=166247  y=18032
x=185313  y=20100
x=1100703  y=119388
x=1226937  y=133080
x=4563527  y=494984
x=6362297  y=690088
x=27105977  y=2940056
x=30214623  y=3277236

10.71875

ysr

蔡家雄 发表于 2025-4-6 23:14
求 \(x^2 - 85*y^2= - (171*339)\) 的正整数解，，

x=154  y=31
x=186  y=33
x=1446  y=159
x=1614  y=177
x=6034  y=655
x=8414  y=913
x=35854  y=3889
x=39966  y=4335
x=207246  y=22479
x=231014  y=25057
x=984214  y=106753
x=1372154  y=148831
x=5103654  y=553569
x=5688966  y=617055
x=33790746  y=3665121
x=37666034  y=4085455

11.5

ysr

蔡家雄 发表于 2025-4-7 12:39
求 \(x^2 - 13*y^2= (51*103)\) 的正整数解，，

x=155  y=38
x=181  y=46
x=235  y=62
x=389  y=106
x=4421  y=1226
x=7435  y=2062
x=9829  y=2726
x=11675  y=3238
x=189515  y=52562
x=225109  y=62434
x=297595  y=82538
x=500501  y=138814
x=5738069  y=1591454
x=9650395  y=2676538
x=12757861  y=3538394
x=15153995  y=4202962

5.445313

ysr

蔡家雄 发表于 2025-4-7 12:40
求 \(x^2 - 13*y^2= - (51*103)\) 的正整数解，，

x=112  y=37
x=200  y=59
x=268  y=77
x=320  y=91
x=5260  y=1459
x=6248  y=1733
x=8260  y=2291
x=13892  y=3853
x=159268  y=44173
x=267860  y=74291
x=354112  y=98213
x=420620  y=116659
x=6827800  y=1893691
x=8110172  y=2249357
x=10721680  y=2973659
x=18031928  y=5001157

5.455078

ysr

蔡家雄 发表于 2025-4-7 12:47
求 \(x^2 - 53*y^2= (211*423)\) 的正整数解，，

x=20139  y=2766
x=23109  y=3174
x=127941  y=17574
x=146811  y=20166

5.457031

ysr

蔡家雄 发表于 2025-4-7 12:48
求 \(x^2 - 53*y^2= - (211*423)\) 的正整数解，，

x=288  y=57
x=348  y=63
x=7330248  y=1006887
x=8411388  y=1155393
x=46570812  y=6396993
x=53439552  y=7340487

5.517578

ysr

蔡家雄 发表于 2025-4-7 23:53
求 \(x^2 - 85*y^2= (339*679)\) 的正整数解，，

x=1189  y=118
x=1291  y=130
x=1429  y=146
x=2789  y=298
x=17579  y=1906
x=34171  y=3706
x=68171  y=7394
x=75989  y=8242
x=432821  y=46946
x=482459  y=52330
x=962539  y=104402
x=1871291  y=202970
x=11881061  y=1288682
x=23703541  y=2571010
x=26421979  y=2865866
x=28889461  y=3133502

5.585938