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

ysr

蔡家雄 发表于 2025-4-6 06:58
求 \(x^2 - 29*y^2= 115\) 的正整数解，，

x=12  y=1
x=684  y=127
x=824  y=153
x=64832  y=12039
x=170392  y=31641
x=13406944  y=2489607
x=16151364  y=2999233

5.671875

ysr

蔡家雄 发表于 2025-4-6 07:01
求 \(x^2 - 53*y^2= 211\) 的正整数解，，

x=2468  y=339
x=2832  y=389

5.515625

ysr

蔡家雄 发表于 2025-4-6 07:15
求 \(x^2 - 85*y^2= 339\) 的正整数解，，

x=268  y=29
x=6592  y=715
x=7348  y=797
x=180952  y=19627

5.5625

Treenewbee

蔡家雄 发表于 2025-4-6 21:46
求 \(x^2 - 13*y^2= (27*51)\) 的正整数解，，

{{47,8},{57,12},{135,36},{177,48},{463,128},{967,268},{2553,708},{3375,936},{8913,2472},{11783,3268},{49223,13652},{65073,18048},{171855,47664},{227193,63012},{600007,166412},{1254703,347992},{3313617,919032},{4380615,1214964},{11569017,3208668},{15294287,4241872},{63891407,17720288},{84464697,23426292},{223067655,61867836},{294896337,81789528},{778808623,216002648},{1628603527,451693348},{4301072313,1192902828},{5686034895,1577022336},{15016575153,4164848592},{19851972743,5505946588},{82930997063,23000920172},{109635111633,30407308968},{289541644335,80304403464},{382775218233,106162744332},{1010892992647,280371270692},{2113926123343,586297617712},{5582788548657,1548386951712},{7380468913095,2046973777164},{19491502979577,5405970263748},{25767845326127,7146714429352},{107644370296367,29855176662968},{142306290434937,39468663614172},{375824831279175,104235053828436},{496841938370097,137799160353408},{1312138325647183,363921693355568},{2743874479495687,761013856096828},{7246455235084473,2009805070419348},{9579842963162415,2656970385736536},{25299955850915793,7016945237496312},{33446643381340103,9276429823352308},{139722309713687303,38751996307612292},{184713455349436593,51230294963886288},{487820341458724815,135297019564906464},{644900453229167673,178863203975979252},{1703154535797050887,472370077604256572},{3561546960459278383,987795398916065032},{9405893312351097297,2608725433017361992},{12434628785715901575,3448745513712246564},{32839323202985719737,9107989512299949228},{43413717341134127567,12040798763996866432}}

Treenewbee

蔡家雄 发表于 2025-4-6 21:47
求 \(x^2 - 13*y^2= - (27*51)\) 的正整数解，，

{{14,11},{66,21},{90,27},{246,69},{326,91},{1366,379},{1806,501},{4770,1323},{6306,1749},{16654,4619},{34826,9659},{91974,25509},{121590,33723},{321114,89061},{424514,117739},{1773394,491851},{2344434,650229},{6191550,1717227},{8185254,2270181},{21616906,5995451},{45204134,12537371},{119382186,33110661},{157823730,43772427},{416805726,115601109},{551018846,152825131},{2301864046,638422219},{3043073526,843996741},{8036627130,2228959323},{10624453386,2946693189},{28058727334,7782090779},{58674931106,16273497899},{154957985454,42977612469},{204855079950,56816576523},{541013511234,150050150421},{715222037594,198366902299},{2987817758314,828671548411},{3949907092314,1095507119589},{10431535823190,2893187484027},{13790532309774,3824805489141},{36420206462626,10101147835691},{76160015371454,21122987735531},{201135345737106,55784907874101},{265901735951370,73747872554427},{702235120776006,194764979645349},{928357653778166,257480086358971},{3878185148427526,1075615031415259},{5126976362750046,1421967397229781},{13540125461873490,3755355125307723},{17900100313633266,4964594578211829},{47273399929761214,13111282108636139},{98855641277216186,27417621807221339},{261073523808778134,72408767442970629},{345140248409798310,95724681759069723},{911500645753744554,252804793529512581},{1205007519382021874,334208953727042059},{5033881334841170434,1396147482105457771},{6654811368942467394,1845712586097136149},{17575072417975966830,4874448059461940427},{23234316416563669494,6444039937713464901},{61360836688623593146,17018434075861872731}}

Treenewbee

蔡家雄 发表于 2025-4-6 21:47
求 \(x^2 - 13*y^2= - (27*51)\) 的正整数解，，

{{14,11},{66,21},{90,27},{246,69},{326,91},{1366,379},{1806,501},{4770,1323},{6306,1749},{16654,4619},{34826,9659},{91974,25509},{121590,33723},{321114,89061},{424514,117739},{1773394,491851},{2344434,650229},{6191550,1717227},{8185254,2270181},{21616906,5995451},{45204134,12537371},{119382186,33110661},{157823730,43772427},{416805726,115601109},{551018846,152825131},{2301864046,638422219},{3043073526,843996741},{8036627130,2228959323},{10624453386,2946693189},{28058727334,7782090779},{58674931106,16273497899},{154957985454,42977612469},{204855079950,56816576523},{541013511234,150050150421},{715222037594,198366902299},{2987817758314,828671548411},{3949907092314,1095507119589},{10431535823190,2893187484027},{13790532309774,3824805489141},{36420206462626,10101147835691},{76160015371454,21122987735531},{201135345737106,55784907874101},{265901735951370,73747872554427},{702235120776006,194764979645349},{928357653778166,257480086358971},{3878185148427526,1075615031415259},{5126976362750046,1421967397229781},{13540125461873490,3755355125307723},{17900100313633266,4964594578211829},{47273399929761214,13111282108636139},{98855641277216186,27417621807221339},{261073523808778134,72408767442970629},{345140248409798310,95724681759069723},{911500645753744554,252804793529512581},{1205007519382021874,334208953727042059},{5033881334841170434,1396147482105457771},{6654811368942467394,1845712586097136149},{17575072417975966830,4874448059461940427},{23234316416563669494,6444039937713464901},{61360836688623593146,17018434075861872731}}

Treenewbee

蔡家雄 发表于 2025-4-6 21:47
求 \(x^2 - 13*y^2= - (27*51)\) 的正整数解，，

{{14,11},{66,21},{90,27},{246,69},{326,91},{1366,379},{1806,501},{4770,1323},{6306,1749},{16654,4619},{34826,9659},{91974,25509},{121590,33723},{321114,89061},{424514,117739},{1773394,491851},{2344434,650229},{6191550,1717227},{8185254,2270181},{21616906,5995451},{45204134,12537371},{119382186,33110661},{157823730,43772427},{416805726,115601109},{551018846,152825131},{2301864046,638422219},{3043073526,843996741},{8036627130,2228959323},{10624453386,2946693189},{28058727334,7782090779},{58674931106,16273497899},{154957985454,42977612469},{204855079950,56816576523},{541013511234,150050150421},{715222037594,198366902299},{2987817758314,828671548411},{3949907092314,1095507119589},{10431535823190,2893187484027},{13790532309774,3824805489141},{36420206462626,10101147835691},{76160015371454,21122987735531},{201135345737106,55784907874101},{265901735951370,73747872554427},{702235120776006,194764979645349},{928357653778166,257480086358971},{3878185148427526,1075615031415259},{5126976362750046,1421967397229781},{13540125461873490,3755355125307723},{17900100313633266,4964594578211829},{47273399929761214,13111282108636139},{98855641277216186,27417621807221339},{261073523808778134,72408767442970629},{345140248409798310,95724681759069723},{911500645753744554,252804793529512581},{1205007519382021874,334208953727042059},{5033881334841170434,1396147482105457771},{6654811368942467394,1845712586097136149},{17575072417975966830,4874448059461940427},{23234316416563669494,6444039937713464901},{61360836688623593146,17018434075861872731}}

Treenewbee

蔡家雄 发表于 2025-4-6 21:47
求 \(x^2 - 13*y^2= - (27*51)\) 的正整数解，，

{{14,11},{66,21},{90,27},{246,69},{326,91},{1366,379},{1806,501},{4770,1323},{6306,1749},{16654,4619},{34826,9659},{91974,25509},{121590,33723},{321114,89061},{424514,117739},{1773394,491851},{2344434,650229},{6191550,1717227},{8185254,2270181},{21616906,5995451},{45204134,12537371},{119382186,33110661},{157823730,43772427},{416805726,115601109},{551018846,152825131},{2301864046,638422219},{3043073526,843996741},{8036627130,2228959323},{10624453386,2946693189},{28058727334,7782090779},{58674931106,16273497899},{154957985454,42977612469},{204855079950,56816576523},{541013511234,150050150421},{715222037594,198366902299},{2987817758314,828671548411},{3949907092314,1095507119589},{10431535823190,2893187484027},{13790532309774,3824805489141},{36420206462626,10101147835691},{76160015371454,21122987735531},{201135345737106,55784907874101},{265901735951370,73747872554427},{702235120776006,194764979645349},{928357653778166,257480086358971},{3878185148427526,1075615031415259},{5126976362750046,1421967397229781},{13540125461873490,3755355125307723},{17900100313633266,4964594578211829},{47273399929761214,13111282108636139},{98855641277216186,27417621807221339},{261073523808778134,72408767442970629},{345140248409798310,95724681759069723},{911500645753744554,252804793529512581},{1205007519382021874,334208953727042059},{5033881334841170434,1396147482105457771},{6654811368942467394,1845712586097136149},{17575072417975966830,4874448059461940427},{23234316416563669494,6444039937713464901},{61360836688623593146,17018434075861872731}}

Treenewbee

蔡家雄 发表于 2025-4-6 21:48
求 \(x^2 - 29*y^2= (59*115)\) 的正整数解，，

{{191,32},{481,88},{737,136},{887,164},{37567,6976},{45257,8404},{69641,12932},{183031,33988},{3560951,661252},{9358921,1737908},{14401417,2674276},{17349407,3221704},{736387447,136743716},{887126977,164735344},{1365102401,253493152},{3587773471,666232808},{69801761311,12961861672},{183453568961,34066472528},{282296575297,52421158016},{340083075127,63151841644},{14434666698527,2680450314056},{17389462957897,3229142204684},{26758737194761,4968972752572},{70327535395511,13059495468428},{1368254121657271,254078411833292},{3596056849414601,667770992755948},{5533577454570377,1027559536755356},{6666308421290047,1237902396683984},{282948335888138807,52542186919381996},{340868252013570017,63297645331480424},{524524765126602721,97401803642423192},{1378560345235033151,255992229505892848},{26820517222924064831,4980445015794328112},{70489906178771439841,13089646965935620168}}

Treenewbee

蔡家雄 发表于 2025-4-6 21:48
求 \(x^2 - 29*y^2= (59*115)\) 的正整数解，，

{{191,32},{481,88},{737,136},{887,164},{37567,6976},{45257,8404},{69641,12932},{183031,33988},{3560951,661252},{9358921,1737908},{14401417,2674276},{17349407,3221704},{736387447,136743716},{887126977,164735344},{1365102401,253493152},{3587773471,666232808},{69801761311,12961861672},{183453568961,34066472528},{282296575297,52421158016},{340083075127,63151841644},{14434666698527,2680450314056},{17389462957897,3229142204684},{26758737194761,4968972752572},{70327535395511,13059495468428},{1368254121657271,254078411833292},{3596056849414601,667770992755948},{5533577454570377,1027559536755356},{6666308421290047,1237902396683984},{282948335888138807,52542186919381996},{340868252013570017,63297645331480424},{524524765126602721,97401803642423192},{1378560345235033151,255992229505892848},{26820517222924064831,4980445015794328112},{70489906178771439841,13089646965935620168}}