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Integral Points on Conic Curves: x^2-Dy^2=±1(D \in [9000,9999])


[2003.08.16]x2-Dy2=±1 (D \in [9000,9999])の整点


9000≦D≦9999かつ平方数でない整数Dについて、Pell方程式
     x2-Dy2 = ±1
の基本解を求めと、以下のようになる。

D fundamental solution [x,y] of x2-Dy2=-1 fundamental solution [x,y] of x2-Dy2=1
9000 - [39480499, 416161]
9001 [29384466921266370037322991640236833565466451463888089268841990011060, 309722271355344700885435418592835727897510979705380767376055343949] [1726893792493995006683993838974761977959776675285196663306488830201492514711080925161662600712136108240425893542880243573769637844647201, 18202047674841225865402802761777035233473605428628865602838998772731574643969501174549483652354138832495727012773263531125581228151880]
9002 - [52536732283853, 553724261298]
9003 - [24051697562, 253484909]
9004 - [66488457799, 700694190]
9005 - [2930601609, 30882676]
9006 - [949, 10]
9007 - [64149582002144305857124164253731109808, 675933155113774891644407319428556153]
9008 - [9281213767, 97789131]
9009 - [2251038838049, 23716177640]
9010 [47873938497, 504355501] [4583827974429077238019, 48290968470995243994]
9011 - [280928905147446773041667882041849226427455530, 2959442673451863506934007766753927677065303]
9012 - [32049873888048012151, 337610335442209830]
9013 [12584381939318944033752282041810283518085755797922572847596210405182, 132555333051058436289967398341383243510290642001852191020027779625] [316733337589313653593819548701297852730476702791552733749386402672377415373749786933927822887211277109251862302606058867110569224906249, 3336253878416294566199459327551220009283569264631264106762658521557301088548608634820578904470229513501848602390500133484234108033500]
9014 - [5084717112026810384813527464062245, 53555985969485940409515755015346]
9015 - [1804, 19]
9016 - [57643991108495, 607081629258]
9017 - [49544678326622621605094367, 521754229434771234401192]
9018 - [206869247, 2178416]
9019 - [2510662054201314751295235996221511190, 26436810943837050700606778082313611]
9020 - [3609, 38]
9021 - [428545, 4512]
9022 - [431023078597582635893, 4537839312076580622]
9023 - [9024, 95]
9024 - [95, 1]
9026 [95, 1] [18051, 190]
9027 - [9026, 95]
9028 - [4940078897198882821249, 51992189853635164200]
9029 [428830, 4513] [367790337801, 3870619580]
9030 - [3611, 38]
9031 - [156173578460397153055749671587288132542010889205940, 1643386217643155840214667359173081835963137043723]
9032 - [2426397123, 25531123]
9033 - [86337034347999835223, 908408358394131804]
9034 [20714077841411235, 217934286428833] [858146041640087857766112768450451, 9028615546798517750138228277510]
9035 - [1806, 19]
9036 - [27009633024199, 284138819910]
9037 - [974759566903254242635777046972521399, 10253812345591982822523481339289340]
9038 - [847333584363912643392783, 8912883946423875211676]
9039 - [185280467997215, 1948809759304]
9040 - [435259412378569, 4577875275987]
9041 [190808234837301321572271806857156957818532, 2006729704253042700802302915031513223905] [72815564963453459382432153550958679593873891760254802097632612308609292648485270049, 765801105328205600552169215456416078087736937222377742551497532368488078548814920]
9042 - [136796417, 1438608]
9043 - [84545683840978739384400273277544534884255192470026, 889068402772249488424830285872759539610216260665]
9044 - [951, 10]
9045 - [2950149761, 31019856]
9046 - [240024708553528969195337916418863338146751949587463025938529913115640552749308717163302885, 2523641492907273141666863705738570492343759776998792971799800869482978012639609651230162]
9047 - [1024523899687, 10771341588]
9048 - [97499, 1025]
9049 [1093971168, 11500205] [2393545832830568449, 25161785392178880]
9050 [27493, 289] [1511730099, 15890954]
9051 - [1248568005258190, 13123930427157]
9052 - [24592297087, 258479928]
9053 - [337713507564644417474726219852996599, 3549377331638927710584216908748660]
9054 - [14125267563780214605455, 148448713418524973916]
9055 - [1483750262538198213285963896740889, 15592529755029386086931066218068]
9056 - [18282270756422449, 192115289484015]
9057 - [112400491802052179298315391073839353751, 1181071058786460140976848688685796900]
9058 - [1671181878563, 17559314586]
9059 - [273506307232636647545847190553836250, 2873605962195725402739521607990369]
9060 - [486976309471, 5116155492]
9061 [89338551717346290, 938535798571121] [15962753645905915484474559553528201, 167694857958453987445703900982180]
9062 - [1021247, 10728]
9063 - [476, 5]
9064 - [2764743626523751885, 29039886668112021]
9065 - [58542208172352001, 614872677971040]
9066 - [17809461849456587328251951, 187043637243603529037020]
9067 - [1169196508206539318045277504684996650460861963748956026, 12278793674630826000815467289121177493447584983238195]
9068 - [247395611746167171699498247, 2597982588921667279514634]
9069 - [10058249006177282519983178214987258642754601611064807536822825055, 105619153400987278296106564974518757069215237280312078933990264]
9070 - [10456213400938258613848342542410891, 109792024844751656504541381437178]
9071 - [117296907471022320, 1231569652106087]
9072 - [8193151, 86020]
9073 - [117470808603513605143, 1233259594210638876]
9074 [1078613682895, 11323131157] [2326814953856631231162051, 24426568398309784919030]
9075 - [189750626, 1991865]
9076 - [30021853822377566529035247049, 315130372212815969679815970]
9077 - [1804517678601, 18940436060]
9078 - [435389957, 4569654]
9079 - [217210457691542063960, 2279616137316437109]
9080 - [24618466891, 258355719]
9081 - [583201, 6120]
9082 - [2046707069101907597, 21476570936149962]
9083 - [25126013781663, 263638563464]
9084 - [2737623170905, 28723350994]
9085 - [1946719, 20424]
9086 - [7435, 78]
9087 - [12583, 132]
9088 - [40897, 429]
9089 [285731980, 2997097] [163285528789440801, 1712732920124120]
9090 - [23060456786321, 241872205116]
9091 - [11200143276309036818809232121055429827148815550306865206323196131670188145446568520932370, 117467506353600051516637202442967875470045730004968347060336814269122743114372347587167]
9092 - [765910128188622849, 8032451260855520]
9093 - [1188151, 12460]
9094 - [108262486044746017630455365, 1135273552784213081356914]
9095 - [26605016, 278973]
9096 - [22036808705, 231059312]
9097 - [6679051718784831360454427626790258791812765141406430473406564567, 70027030273410247727899702179540900514499442073311909657688452]
9098 [20798828090507, 218054924485] [865182499876926119567034099, 9070573777304001260727790]
9099 - [2392898905826, 25085774765]
9100 - [4954951, 51942]
9101 - [54264951, 568820]
9102 - [7433384213, 77914478]
9103 - [1728250909663520461199478640464664637471558766700448, 18114006647283718226567570715136551913578825501399]
9104 - [16760473211643448449, 175658897131003580]
9105 - [4186116818400041, 43870377208404]
9106 [69836301535629855, 731842132644389] [9754218024350833687264103134642051, 102218295703663943112587693267190]
9107 - [40146290526, 420685705]
9108 - [3222617399, 33767370]
9109 [14305924709281590481348512639330, 149892735017204636479857799417] [409318963575267118261930148827931582909096978990465525325697801, 4288708363248851433061400366090115400041485983269808810541220]
9110 - [2702257318512719, 28311802055244]
9111 - [61434385295099179903731265012763815, 643618462895962748311577541941772]
9112 - [14945957, 156573]
9113 - [3097413376617, 32446546924]
9114 - [1688175067501, 17683285950]
9115 - [1211005412710716790006295446, 12684336294479445354101211]
9116 - [181556905575, 1901562542]
9117 - [191159785254200303902359515365981601, 2002029887363053063559931047754360]
9118 - [1288900496447, 13498005384]
9119 - [507472391449, 5314211220]
9120 - [191, 2]
9121 - [19100114120251334391453369938121739541965607615782071039847775734754815, 199992971975690633173946046932679821008042375794900184039185567312288]
9122 - [896731192379730723, 9388954681173382]
9123 - [1524645172528426150226, 15962464542307130895]
9124 - [2981649830743654269669907724743299862819650512057127554474550049, 31215047464388711559691260897356246272577180678380801795855740]
9125 [7911247523702795818, 82818724228772641] [125175674762587237756296879179596578249, 1310398853942204588962989860735230676]
9126 - [403988416827863757605, 4228912321466099718]
9127 - [2871973071056288844711536689861595599063199885974808, 30061893934883309249839054034983831216334112270963]
9128 - [3570351, 37370]
9129 - [84532100216504153385338803799, 884728577735400511989341340]
9130 - [109698826451573510911, 1148065305532298928]
9131 - [193138087863996644255, 2021197516931212248]
9132 - [12747007282038151, 133390617340970]
9133 [21203706342027618, 221873304716885] [899194325277884457775014949507849, 9409072796704081371828681859860]
9134 - [1185780492335851084418643417976241295, 12407200421159055187928228581474156]
9135 - [352871, 3692]
9136 - [65612063992983395551353492198003600753799, 686444855120994239524235280899445559155]
9137 [34548492047245559573503014232, 361432568329002341881916585] [2387196605477179352307054995507397216114597418379189099649, 24973900425060149430561478028712447168724303821383675440]
9138 - [1849600000001, 19348720000]
9139 - [6133222126400656705306370, 64156306736230764125721]
9140 - [93197234874249, 974832341990]
9141 - [2093900302904402015, 21900757946039208]
9142 - [143831001590902323065627903980351, 1504291135393050122896700927640]
9143 - [2008, 21]
9144 - [130049, 1360]
9145 - [206645617777751, 2160898385220]
9146 [535581787565, 5600285941] [573695702342641577258451, 5998822310311836247330]
9147 - [1905626, 19925]
9148 - [23239871781927470022429904687994906036342518218751, 242980068234608049389310698331287993810643984000]
9149 - [814227543415, 8512536276]
9150 - [1648655611249, 17235321860]
9151 - [1800632184599033375527959920, 18823081853679508648771743]
9152 - [287, 3]
9153 - [2900932297217, 30321861664]
9154 - [331883645970275, 3468809088666]
9155 - [1772409, 18524]
9156 - [2883049, 30130]
9157 [11476806675780112284925915529408231104304326654467761719818, 119934591158260551772514860608279271082251449500141364625] [263434182946461902766766147267778847778755605993417516861180590773144283458958166037288044144971591768942186267906249, 2752932232924166259844215557485622974122177805195698894754071781826599459007387029852063324354059431802222853276500]
9158 - [15216209317, 159003306]
9159 - [68447127551, 715206080]
9160 - [3609620264130499, 37714971097605]
9161 [437598551832240207733212615750145571432, 4571981185439461579548096268568626325] [382984985131347639337218867644375695893692702513145101062740815398083629061249, 4001384691505114513905790674004622633500528178810220178848498020548806294800]
9162 - [15155578752298003, 158335166058778]
9163 - [64031518226017, 668921193624]
9164 - [13753452193775865567478960199, 143671022274761929466615670]
9165 - [11493123086719, 120052669968]
9166 - [1382967871852175, 14445153611508]
9167 - [55959967922139648, 584472175924297]
9168 - [383, 4]
9169 [208919205725823329386786046254620, 2181812269483345208756949562273] [87294469042217782837400924118671577020711971274482084259742688801, 911644972766632974574804423269249664686152240167397880207902520]
9170 - [818749, 8550]
9171 - [6089923321730, 63592145513]
9172 - [3996915809449797781026127104343692038269891422048887887519392649, 41734284992203724725314074028958510310977848561787990047840510]
9173 [8888666551262318, 92807039191225] [158016786119059100131438493466249, 1649861649961465414243077519100]
9174 - [4154219888684645, 43372066274674]
9175 - [27522711992139369632096475575024, 287334774302391463611588251013]
9176 - [3294555, 34393]
9177 - [10116482473, 105603708]
9178 [475634475367175181, 4964771890158973] [452456308315615948061495127084765523, 4722833346586923613574016060098226]
9179 - [2441061006483602167256766770, 25478916083001874368563541]
9180 - [533729791, 5570576]
9181 [3139064344164259350, 32760854748226189] [19707449913606783347068427868124845001, 205676862049002407686586126916234300]
9182 - [367493741714198611974399, 3835140716152159462960]
9183 - [432580903544010151, 4514140283277540]
9184 - [575, 6]
9185 - [27740581598393751, 289451618132900]
9186 - [266479464881227282003414928378410385, 2780356768161411180167061023804572]
9187 - [7573060379925195137957582608018562, 79010454724715567912469573020367]
9188 - [387430169379776126085928364346126849, 4041875603769570412637362327743760]
9189 - [198723867690977573219668252231077415636351801801, 2073079253071587609062469834339810871992228180]
9190 - [1674907208954681593707836451919, 17471612787176317414342058268]
9191 - [694576, 7245]
9192 - [767, 8]
9193 [18974074160818778125133440164, 197893697767910294182803373] [720030980520501638668811409507028311759154062554736693793, 7509699394813974841772122078648104433163314306145746344]
9194 [1232331971285150084765, 12852140544735499673] [3037284174903087946119699228942973370210451, 31676207385455401902881932978521159563690]
9195 - [2346576652934, 24471403533]
9196 - [772362118440199, 8054182827990]
9197 [9686, 101] [187637193, 1956572]
9198 - [2093057, 21824]
9199 - [1053344927816119107196375157694929519417266955491964582169476720418214485349747839063034640, 10982476911143937022341031003918681914153735132652023268221576527593244593149235240351449]
9200 - [1151, 12]
9201 - [101672442664470309534530811567233327697752980402631690455, 1059950885935564329058740584497933931268858708980349332]
9202 - [145824644455900485063358890257, 1520161788692321322220516932]
9203 - [175572488813576978762, 1830171358293114441]
9204 - [1535, 16]
9205 - [1625154094241, 16938800376]
9206 - [1615311791693539406185470444347021813723525, 16835300711031874823707036210037515503702]
9207 - [130976, 1365]
9208 - [2303, 24]
9209 [1996606662593618093329397086244137673332, 20805889111743814536018205933879168805] [7972876330226451848005612812809792927000414784279450928336729249287924687964449, 83082353643383429528885230520829858809739562608165803307518397470549549616520]
9210 - [3071, 32]
9211 - [1219560087172162077059694764390, 12707198423889621199172743797]
9212 - [4607, 48]
9213 - [6143, 64]
9214 - [9215, 96]
9215 - [96, 1]
9217 [96, 1] [18433, 192]
9218 - [9217, 96]
9219 - [6145, 64]
9220 - [4609, 48]
9221 [422202046718477782, 4396745454839345] [356509136506543391296188534455279049, 3712629859866671965422847523865580]
9222 - [3073, 32]
9223 - [212218881100250456640911444951109848, 2209774288594140617694359508227331]
9224 - [2305, 24]
9225 - [8396801, 87424]
9226 - [14590787990856007583505366594123204397845295, 151904983520745233765099215003212075283932]
9227 - [203255570105625696611912629146085284026, 2115983104782511642586702447075786595]
9228 - [1537, 16]
9229 - [3363486101839799, 35011628731260]
9230 - [898593749, 9353250]
9231 - [1040809346824, 10832951735]
9232 - [1153, 12]
9233 - [2913887629292757968892563026399, 30325039966512500036622801720]
9234 - [4307559425, 44826656]
9235 - [15295006, 159159]
9236 - [14554556667841571687399049, 151445725218740551682770]
9237 - [3314215749015825785119351, 34483814873885658748740]
9238 - [815892535186633489480399, 8488754637192682410780]
9239 - [2029344175600926518518185077260474916774280, 21112673221657620410607133242882858038021]
9240 - [769, 8]
9241 [2507372934655243693713650013375626883548839506168622856164206898322396114581366668, 26083114540479362207174160452327440784976324993926454237786908779496215983953365] [12573838066883297924025856555850154472486093484157078993537834939845467061258394878207218793460782082220079247310394068809320671583968898005826866965287013322844449, 130800190900621192997821801731887110424328332042516650805528199345533111208104700959904643449309336825053218088643171196800540988864315210797366076845838554875640]
9242 [510137369981, 5306450981] [520480272502263359880723, 5414037894760874802722]
9243 - [133150393, 1384956]
9244 - [321428873065571841201588628335279000321256096514041113993166182574306661667484776224427638556799, 3343142720509771911461680187445462659340201013290449597206370866344191723294186054872674618840]
9245 - [1929027937031380914713107361, 20062500454410937648803144]
9246 - [13513617936299, 140538298630]
9247 - [141849134395358174207001706688, 1475116297127845677540455313]
9248 - [577, 6]
9249 - [637399174779228272682057872657456864140627177981921885774295, 6627719306656877942785467660999142606908415729429034062324]
9250 [59822398683807, 622003683337] [7157438768568706971928026499, 74419504654764909635247918]
9251 - [15778745887395759850, 164050720284812193]
9252 - [526337, 5472]
9253 - [1909480958047, 19850618856]
9254 - [813750269225500824699, 8459143603849274830]
9255 - [15897837555736, 165253186867]
9256 - [283149908724275862475699, 2943098199287419228785]
9257 [71757909602329786044451232, 745821067378316592596485] [10298395180992266625471148155884348235937232052635649, 107037121464892709132308647810552354058331674239040]
9258 - [11215338653113245613, 116561144655043686]
9259 - [109611891887841598152401152015863455, 1139136143198572744755713394307656]
9260 - [34601968561276871, 359579822634942]
9261 - [97379496466615, 1011902298628]
9262 - [5702570620811392503440577225077, 59254083338490155165868469338]
9263 - [59860621748052, 621964205359]
9264 - [385, 4]
9265 [666952209619777068, 6929023015392305] [889650499833406101128820076037353249, 9242654421244376779872213325323480]
9266 - [119555, 1242]
9267 - [1236985242981602, 12849757657753]
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9946 [173885517916953164732782555451597979165, 1743569188505657755233039736656744709] [60472346682494080138990458640060056388378423773759846669343335871823548194451, 606362862734696083049177932424040186050707725868033541116162357703411975970]
9947 - [125046060424377, 1253787555332]
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9949 [3431546270623363128596014118116144221075051039537067641511872618579455226741550509978502410879762136834818, 34403303269449939153283126077708664857428452182230098434142453222430571308633791476247185645245170282525] [23551019614858223475933893515741198183163217312913587552899320396564478041197360918469501097146448985821854465768234479384482435117587576296319428592757548743265811454938493105633433315887574461850060798834186249, 236113054062810988826514929828649213339688520849720684015415366388626019230322623673232286474879711003505448178417385617250641629212134427833135509077013929303770208680820795381507114806491325360400076633910900]
9950 - [399, 4]
9951 - [237346876876, 2379305225]
9952 - [13804370063, 138376203]
9953 [1696, 17] [5752833, 57664]
9954 - [51106049, 512240]
9955 - [899126911, 9011568]
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9959 - [2426158073970669480, 24311470443585619]
9960 - [499, 5]
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9962 - [31138867, 311982]
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9965 [1965165618129578242, 19686137118519029] [7723751813357214672110715265599621129, 77373039638196163818267126842734036]
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9969 - [69477291214609898838425037536970877238130361957505250282455, 695852320433520145241963296042428639505200732746235179564]
9970 [17136540368198968275663, 171623031595451439541] [587322031581825662399480582605376615116179139, 5882050018096281155077322863615047732381366]
9971 - [751810445714495508290, 7529029476275228487]
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9973 [186718093482, 1869706745] [69727292867105781768649, 698216157593671872180]
9974 - [1719288109263505431842025445, 17215275516656285600570274]
9975 - [799, 8]
9976 - [103140178995886814699, 1032641704399717965]
9977 - [12750532537556216287701436832983, 127652209924210109640047989212]
9978 - [50323145063149, 503785920270]
9979 - [574619598100480625074, 5752239006216930405]
9980 - [999, 10]
9981 - [1109164308079499990841149135688424315845272973507866496176801, 11102195180847411885850512058959825600519458603929299899160]
9982 - [58755168396863, 588081195432]
9983 - [993345173223277017, 9941905946857156]
9984 - [3120001, 31225]
9985 [2030525335128816474207251508, 20320499445302989009314473] [8246066273199984907805980278898195706052877543136548129, 82522577892317562054627858935732613116232105150950568]
9986 - [5397592785985, 54013750728]
9987 - [180901128102602, 1810188286063]
9988 - [19409802197604122787127127, 194214585707081824104534]
9989 - [175608995858278095552686089827219340297975, 1757056605616947588621886557316228078404]
9990 - [1999, 20]
9991 - [1287746074520, 12883259517]
9992 - [2499, 25]
9993 - [61508786157972776212869020804494515460494487, 615303255419645369700183146701653918462324]
9994 - [3868785983813978819581748078264416205, 38699471421565110562003054367789886]
9995 - [3999, 40]
9996 - [4999, 50]
9997 [1056881013819720204460013572819482, 10570395816504471539188482748085] [2233994954745199219608947478540746520621707535213601737381917496649, 22343301294045950038591020734822406588061732170848426457972383940]
9998 - [9999, 100]
9999 - [100, 1]


[参考文献]


Last Update: 2005.06.12
H.Nakao

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