Examples of solutions to Pell's equation P^2-DQ^2 = 1 in polynomials, where deg(P) > 2 ====================================================================================== D = 4x^2+4x+5, P = 32x^6+96x^5+168x^4+176x^3+120x^2+48x+9, Q = 16x^5+40x^4+56x^3+44x^2+20x+4 D = 4x^2+12x+5, P = 4x^3+18x^2+24x+9, Q = 2x^2+6x+4 D = 16x^2+16x+12, P = 32x^4+64x^3+64x^2+32x+7, Q = 8x^3+12x^2+8x+2 D = 16x^2+48x+28, P = 32x^4+192x^3+416x^2+384x+127, Q = 8x^3+36x^2+52x+24 D = 36x^2+28x+5, P = 2916x^3+3402x^2+1296x+161, Q = 486x^2+378x+72 D = 36x^2+36x+21, P = 864x^6+2592x^5+3672x^4+3024x^3+1512x^2+432x+55, Q = 144x^5+360x^4+408x^3+252x^2+84x+12 D = 36x^2+44x+13, P = 2916x^3+5346x^2+3240x+649, Q = 486x^2+594x+180 D = 36x^2+108x+69, P = 864x^6+7776x^5+28728x^4+55728x^3+59832x^2+33696x+7775, Q = 144x^5+1080x^4+3192x^3+4644x^2+3324x+936 D = 64x^2+64x+32, P = 128x^4+256x^3+224x^2+96x+17, Q = 16x^3+24x^2+14x+3 D = 64x^2+96x+52, P = 2048x^6+9216x^5+18048x^4+19584x^3+12384x^2+4320x+649, Q = 256x^5+960x^4+1504x^3+1224x^2+516x+90 D = 64x^2+160x+116, P = 2048x^6+15360x^5+48768x^4+83840x^3+82272x^2+43680x+9801, Q = 256x^5+1600x^4+4064x^3+5240x^2+3428x+910 D = 64x^2+224x+180, P = 32x^3+168x^2+288x+161, Q = 4x^2+14x+12 D = 81x^2-27x, P = 864x^3-432x^2+54x-1, Q = 96x^2-32x+2 D = 81x^2+27x, P = 864x^3+432x^2+54x+1, Q = 96x^2+32x+2 D = 81x^2+54x, P = 108x^3+108x^2+27x+1, Q = 12x^2+8x+1 D = 81x^2+54x+18, P = 648x^4+864x^3+504x^2+144x+17, Q = 72x^3+72x^2+28x+4 D = 81x^2+54x+27, P = 2916x^6+5832x^5+5832x^4+3456x^3+1269x^2+270x+26, Q = 324x^5+540x^4+432x^3+192x^2+47x+5 D = 81x^2+108x+27, P = 108x^3+216x^2+135x+26, Q = 12x^2+16x+5 D = 81x^2+108x+45, P = 648x^4+1728x^3+1800x^2+864x+161, Q = 72x^3+144x^2+100x+24 D = 81x^2+108x+54, P = 2916x^6+11664x^5+20412x^4+19872x^3+11313x^2+3564x+485, Q = 324x^5+1080x^4+1512x^3+1104x^2+419x+66 D = 81x^2+216x+126, P = 162x^4+864x^3+1692x^2+1440x+449, Q = 18x^3+72x^2+94x+40 D = 81x^2+270x+207, P = 162x^4+1080x^3+2664x^2+2880x+1151, Q = 18x^3+90x^2+148x+80 D = 100x^2-44x+5, P = 7812500000x^6-10312500000x^5+5690625000x^4-1680250000x^3+279975000x^2-24961200x+930249, Q = 781250000x^5-859375000x^4+379375000x^3-84012500x^2+9332500x-416020 D = 100x^2+44x+5, P = 7812500000x^6+10312500000x^5+5690625000x^4+1680250000x^3+279975000x^2+24961200x+930249, Q = 781250000x^5+859375000x^4+379375000x^3+84012500x^2+9332500x+416020 D = 100x^2+92x+21, P = 62500x^3+86250x^2+39600x+6049, Q = 6250x^2+5750x+1320 D = 100x^2+108x+29, P = 62500x^3+101250x^2+54600x+9801, Q = 6250x^2+6750x+1820 D = 144x^2-80x+12, P = 209952x^4-233280x^3+98496x^2-18720x+1351, Q = 17496x^3-14580x^2+4104x-390 D = 144x^2+80x+12, P = 209952x^4+233280x^3+98496x^2+18720x+1351, Q = 17496x^3+14580x^2+4104x+390 D = 256x^2+384x+176, P = 512x^4+1536x^3+1792x^2+960x+199, Q = 32x^3+72x^2+56x+15 D = 324x^2-189x+27, P = 55296x^3-48384x^2+14040x-1351, Q = 3072x^2-1792x+260 D = 324x^2-27x, P = 55296x^3-6912x^2+216x-1, Q = 3072x^2-256x+4 D = 324x^2+27x, P = 55296x^3+6912x^2+216x+1, Q = 3072x^2+256x+4 D = 324x^2+189x+27, P = 55296x^3+48384x^2+14040x+1351, Q = 3072x^2+1792x+260 D = 324x^2+216x+72, P = 648x^4+864x^3+504x^2+144x+17, Q = 36x^3+36x^2+14x+2 D = 324x^2+432x+180, P = 648x^4+1728x^3+1800x^2+864x+161, Q = 36x^3+72x^2+50x+12 D = 576x^2-352x+52, P = 23328x^3-21384x^2+6480x-649, Q = 972x^2-594x+90 D = 576x^2-64x, P = 839808x^4-186624x^3+12960x^2-288x+1, Q = 34992x^3-5832x^2+270x-3 D = 576x^2+64x, P = 839808x^4+186624x^3+12960x^2+288x+1, Q = 34992x^3+5832x^2+270x+3 D = 576x^2+224x+20, P = 23328x^3+13608x^2+2592x+161, Q = 972x^2+378x+36 D = 576x^2+288x+84, P = 55296x^6+82944x^5+58752x^4+24192x^3+6048x^2+864x+55, Q = 2304x^5+2880x^4+1632x^3+504x^2+84x+6 D = 576x^2+352x+52, P = 23328x^3+21384x^2+6480x+649, Q = 972x^2+594x+90 D = 625x^2+125x, P = 1600000x^5+800000x^4+140000x^3+10000x^2+250x+1, Q = 64000x^4+25600x^3+3360x^2+160x+2 D = 625x^2+250x, P = 50000x^5+50000x^4+17500x^3+2500x^2+125x+1, Q = 2000x^4+1600x^3+420x^2+40x+1 D = 625x^2+250x+50, P = 500000x^6+600000x^5+330000x^4+104000x^3+19650x^2+2100x+99, Q = 20000x^5+20000x^4+8800x^3+2080x^2+262x+14 D = 676x^2-116x+5, P = 745538723919392x^6-383798041307616x^5+82362699437928x^4-9431121412336x^3+607749519000x^2-20897315088x+299537289, Q = 28674566304592x^5-12301219272680x^4+2111864088152x^3-181367719468x^2+7791660500x-133957148 D = 676x^2+116x+5, P = 745538723919392x^6+383798041307616x^5+82362699437928x^4+9431121412336x^3+607749519000x^2+20897315088x+299537289, Q = 28674566304592x^5+12301219272680x^4+2111864088152x^3+181367719468x^2+7791660500x+133957148 D = 729x^2+243x+27, P = 40310784x^6+40310784x^5+17356032x^4+4105728x^3+561816x^2+42120x+1351, Q = 1492992x^5+1244160x^4+428544x^3+76032x^2+6936x+260 D = 784x^2-944x+284, P = 184473632x^4-444242624x^3+401139872x^2-160970880x+24220799, Q = 6588344x^3-11899356x^2+7163212x-1437240 D = 784x^2-624x+124, P = 184473632x^4-293651904x^3+175253792x^2-46475520x+4620799, Q = 6588344x^3-7865676x^2+3129532x-414960 D = 900x^2-1108x+341, P = 45562500x^3-84138750x^2+51791400x-10626551, Q = 1518750x^2-1869750x+575460 D = 900x^2-692x+133, P = 45562500x^3-52548750x^2+20201400x-2588599, Q = 1518750x^2-1167750x+224460 D = 900x^2-100x+5, P = 2125764000x^6-708588000x^5+106288200x^4-9039600x^3+456840x^2-12960x+161, Q = 70858800x^5-19683000x^4+2361960x^3-150660x^2+5076x-72 D = 1156x^2-1460x+461, P = 18643911591352352x^6-70640426271732960x^5+111521769045624168x^4-93900092577147760x^3+44472979024658328x^2-11233793974206480x+1182351890184201, Q = 548350340922128x^5-1731382996856200x^4+2186701353835768x^3-138088371436982\ 0x^2+436009598280964x-55067617520620 D = 1156x^2-852x+157, P = 18643911591352352x^6-41223043276381152x^5+37978311557244648x^4-18660952715066352x^3+5157726719915736x^2-760300715612880x+46698728731849, Q = 548350340922128x^5-1010368707754440x^4+744672775632248x^3-274425775221564x^2+5056\ 5948234468x-3726964292220 D = 1296x^2-1648x+524, P = 1377495072x^4-3503259072x^3+3341176128x^2-1416307680x+225144199, Q = 38263752x^3-72984564x^2+46405224x-9835470 D = 1296x^2-944x+172, P = 1377495072x^4-2006721216x^3+1096369344x^2-266247648x+24248647, Q = 38263752x^3-41806692x^2+15227352x-1848942 D = 1600x^2-1952x+596, P = 500000000000x^6-1830000000000x^5+2791050000000x^4-2270542000000x^3+1039107900000x^2-253651322400x+25801741449, Q = 12500000000x^5-38125000000x^4+46517500000x^3-28381775000x^2+8659232500x-1056880510 D = 1600x^2-1248x+244, P = 500000000000x^6-1170000000000x^5+1141050000000x^4-593658000000x^3+173781900000x^2-27138477600x+1766319049, Q = 12500000000x^5-24375000000x^4+19017500000x^3-7420725000x^2+1448182500x-113076990 D = 1600x^2-864x+116, P = 500000x^3-405000x^2+109200x-9801, Q = 12500x^2-6750x+910 D = 1764x^2-2052x+597, P = 11958872141664x^6-41734023188256x^5+60687166968792x^4-47067379893072x^3+20534471384616x^2-4778191782000x+463287093751, Q = 284735050992x^5-828056015640x^4+963288364584x^3-560325951108x^2+162971995116x-18961078500 D = 1764x^2-1476x+309, P = 11958872141664x^6-30019209661728x^5+31400133152472x^4-17518498932816x^3+5498183760552x^2-920396091888x+64202725495, Q = 284735050992x^5-595619239320x^4+498414811944x^3-208553558724x^2+43636379052x-3652365444 D = 1764x^2-980x+133, P = 5833096416x^6-9721827360x^5+6735837528x^4-2483323920x^3+513797256x^2-56563920x+2588599, Q = 138883248x^5-192893400x^4+106918056x^3-29563380x^2+4077756x-224460 D = 2025x^2-2322x+666, P = 253125000x^4-580500000x^3+499275000x^2-190868400x+27365201, Q = 5625000x^3-9675000x^2+5547500x-1060380 D = 2025x^2-1728x+369, P = 253125000x^4-432000000x^3+276525000x^2-78681600x+8396801, Q = 5625000x^3-7200000x^2+3072500x-437120 D = 2025x^2-1404x+243, P = 1687500x^3-1755000x^2+608175x-70226, Q = 37500x^2-26000x+4505 D = 2304x^2-1664x+304, P = 3359232x^4-4852224x^3+2633472x^2-636480x+57799, Q = 69984x^3-75816x^2+27432x-3315 D = 2500x^2-3956x+1565, P = 1907348632812500000x^6-9054565429687500000x^5+17909937744140625000x^4-18893805777343750000x^3+11211598103109375000x^2-3548252371850970000x+467897169491706249, Q = 38146972656250000x^5-150909423828125000x^4+23879916992187\ 5000x^3-188938057773437500x^2+74743987354062500x-11827507906169900 D = 2500x^2-2125x+450, P = 256000x^3-326400x^2+138600x-19601, Q = 5120x^2-4352x+924 D = 3364x^2-3692x+1013, P = 11322073062575009312x^6-37278026528264210208x^5+51140955173522034408x^4-37418268688858499728x^3+15400019610989760216x^2-3380319808919692080x+309159979019115849, Q = 195208156251293264x^5-535603829429083480x^4+58782707096\ 0023384x^3-322571281800504308x^2+88505859833274484x-9713562669309460 D = 3600x^2-4176x+1212, P = 112500000x^4-261000000x^3+227100000x^2-87835200x+12741151, Q = 1875000x^3-3262500x^2+1892500x-365980 D = 3969x^2-4752x+1422, P = 933897762x^4-2236272192x^3+2007994716x^2-801307584x+119908097, Q = 14823774x^3-26622288x^2+15936466x-3179792 D = 4356x^2-5004x+1437, P = 2711602117486944x^6-9344942834645088x^5+13418781921918648x^4-10276501066129584x^3+4426872133791096x^2-1017054943359840x+97359338210399, Q = 41084880567984x^5-117991702457640x^4+135543251736552x^3-77852280804012x^2+223579\ 40069652x-2568320564040 D = 4624x^2-5008x+1356, P = 223224238112x^4-483523782208x^3+392759841088x^2-141793156640x+19196241799, Q = 3282709384x^3-5332982892x^2+2887940008x-521298370 D = 4900x^2-5692x+1653, P = 7353062500x^3-12812336250x^2+7441610400x-1440734849, Q = 105043750x^2-122022250x+35436240 D = 5476x^2-6412x+1877, P = 210654464186881128992x^6-739983431902637946912x^5+1083084026652272214888x^4-845475644145132975632x^3+371246737714887829656x^2-86940670724439475440x+8483443124159168649, Q = 2846681948471366608x^5-8333146755660337240x^4+9\ 757513753624074008x^3-5712673271250898484x^2+1672282602319314548x-195812321451440260 D = 5625x^2-6625x+1950, P = 2916000x^3-5151600x^2+3033450x-595349, Q = 38880x^2-45792x+13482 D = 5625x^2-6500x+1875, P = 2952450000x^5-8529300000x^4+9854257500x^3-5691465000x^2+1643288625x-189750626, Q = 39366000x^4-90979200x^3+78834060x^2-30354480x+4382103 D = 6084x^2-8676x+3093, P = 20129545545823584x^6-86116339820298528x^5+153505845065067768x^4-145935853277979024x^3+78040603007032536x^2-22257529727621760x+2644971939878399, Q = 258071096741328x^5-920046365601480x^4+1312015769786904x^3-93548623896140\ 4x^2+333506850457404x-47558824204320 D = 6724x^2-9748x+3533, P = 722031689611717954592x^6-3140257990928774518752x^5+5690667191644512947688x^4-5499963440066192844272x^3+2990053601651733202776x^2-866955691889293964880x+104737841197119627849, Q = 8805264507459975056x^5-319131909647233182\ 80x^4+46265586923939129656x^3-33536362439428005148x^2+12154689437608671556x-1762105064815638140 D = 8100x^2-13292x+5453, P = 33215062500x^3-81758261250x^2+67082142600x-18346824649, Q = 369056250x^2-605616750x+248452380 D = 8100x^2-12123x+4536, P = 864000000x^3-1939680000x^2+1451525400x-362074049, Q = 9600000x^2-14368000x+5376020 D = 10816x^2-15296x+5408, P = 104413532288x^4-295323481856x^3+313236027104x^2-147660448416x+26102926097, Q = 1003976272x^3-2129736648x^2+1505942438x-354953001 D = 11664x^2-19792x+8396, P = 9037745167392x^4-30671305273152x^3+39033346592448x^2-22077855862560x+4682840457799, Q = 83682825624x^3-212995175508x^2+180709937928x-51106147830 D = 14400x^2-23264x+9396, P = 364500000x^3-883305000x^2+713512800x-192119201, Q = 3037500x^2-4907250x+1981980 D = 15876x^2-25676x+10381, P = 3099946592415456x^6-15040481615052768x^5+30405810661086168x^4-32783001400655856x^3+19882084643087688x^2-6430909623023088x+866702813296375, Q = 24602750733456x^5-99474084755640x^4+160877305085112x^3-130091275399428x^2+\ 52598107521396x-8506494210348 D = 16900x^2-27708x+11357, P = 301675562500x^3-741907676250x^2+608188682400x-166190249601, Q = 2320581250x^2-3804654750x+1559458160 D = 16900x^2-27156x+10909, P = 182016290019382812500000x^6-877426219840182187500000x^5+1762380668104121690625000x^4-1887937288115775477750000x^3+1137621886040522103975000x^2-365600722008925144357200x+48955885787424879807049, Q = 1400125307841406250\ 000x^5-5624527050257578125000x^4+9037849580021136875000x^3-7261297261983751837500x^2+2916979194975697702500x-468718874370416851740 D = 18496x^2-30176x+12308, P = 1193210341846550528x^6-5840124666235106304x^5+11910121188393187968x^4-12954157306432168576x^3+7925467230469845984x^2-2586065413688484000x+351595324374906249, Q = 8773605454754048x^5-35785077611734720x^4+58382947001927\ 392x^3-47625578332471208x^2+19425164780563348x-3169197810892750 D = 20736x^2-33920x+13872, P = 22039921152x^4-72105914880x^3+88463695104x^2-48236834880x+9863382151, Q = 153055008x^3-375551640x^2+307165608x-83744505 D = 23716x^2-39004x+16037, P = 34447389862889696x^6-169959435935083872x^5+349400584245246072x^4-383090451379036016x^3+236266518089582904x^2-77714559462318240x+10651039195104351, Q = 223684349759024x^5-919693917397640x^4+1512556641754312x^3-12438001\ 66815052x^2+511399389804292x-84106666084760 D = 23716x^2-38228x+15405, P = 833689520356x^3-2015745677022x^2+1624597843176x-436450251511, Q = 5413568314x^2-8726171762x+3516445548 D = 35344x^2-63056x+28124, P = 761961173176352x^4-2718776807141696x^3+3637856213328032x^2-2163390783361920x+482453741980799, Q = 4052984963704x^3-10846184071044x^2+9675149503532x-2876849445960 D = 37636x^2-70052x+32597, P = 22202955551854016009441312x^6-123979283849384434809229152x^5+288453767786956405315463208x^4-357933244654383185033392432x^3+249833335296975798531917496x^2-93003108170493917686314480x+14425580508120741496299849, Q = 114\ 448224494092866028048x^5-532557061208696025812840x^4+991250061123561530293688x^3-922508362511296868642764x^2+429266899135697248336628x-79899577466060066740820 D = 40000x^2-71648x+32084, P = 122070312500000000000x^6-655957031250000000000x^5+1468687910156250000000x^4-1753809469656250000000x^3+1178034102756187500000x^2-422019071663951940000x+62993405228436426249, Q = 610351562500000000x^5-273315429687500000\ 0x^4+4895626367187500000x^3-4384523674140625000x^2+1963390171260312500x-351682559719959950 D = 49284x^2-87084x+38469, P = 5687670533045790482784x^6-30150054827109789286752x^5+66593301943595087100312x^4-78446167393569405435504x^3+51979900994351550858312x^2-18369524027128862517552x+2704887002933487852535, Q = 25620137536242299472x^5-113175\ 881483144854680x^4+199979885716501763064x^3-176680557192723886116x^2+78047899390918244532x-13790933954300947836 D = 50625x^2-91422x+41274, P = 98876953125000x^4-357117187500000x^3+483679546875000x^2-291153624210000x+65723089570001, Q = 439453125000x^3-1190390625000x^2+1074843437500x-323504026900 D = 54756x^2-102068x+47565, P = 10260656807076x^3-28689587962542x^2+26739433666296x-8307279893431, Q = 43848960714x^2-81736717842x+38090361348