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Integral Points on Conic Curves: x^2-Dy^2=±1(D \in [8000,8999])


[2003.08.16]x2-Dy2=±1 (D \in [8000,8999])の整点


8000≦D≦8999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
8000 - [1730726404001, 19350109449]
8001 - [13231974717803657215, 147928729471151168]
8002 - [12574413865763, 140568650922]
8003 - [76574994236478, 855973982369]
8004 - [19742928095, 220677484]
8005 [1759374162, 19664257] [6190794883826404489, 69193571361455268]
8006 - [35850516912378763716875711308113279365, 400670740856704528307861089970811198]
8007 - [3799399, 42460]
8008 - [11325887, 126564]
8009 [1223644706769080929180974893100470848044515000, 13673074780560501523320871214842758079685333] [2994612736807980103094414326704971754979051992821787420135830228061148047198843170450000001, 33461971160981340917421889000756682014869253888253377037949932572795862711179153196990000]
8010 - [179, 2]
8011 - [874018946343860822837210485078038130821495698266254502309463746279984552490, 9765117676022524646156117223741039159787030310298367588081066048007235747]
8012 - [37748095474367777981700414406087, 421720365754856005492518642342]
8013 - [10053994998895514798281053751, 112315861720136641776524700]
8014 - [37282060858119845133646041844456463083136145935, 416461867253815981452705744479936600905883004]
8015 - [413344, 4617]
8016 - [11242731902975, 125572054608]
8017 [47029057795634375796, 525243076136138401] [4423464554290236907946137384581101267233, 49403373968726479286530474395001084392]
8018 - [17255449601, 192705120]
8019 - [250283080090, 2794932889]
8020 - [32724809, 365418]
8021 [5612192318, 62664025] [62993405228436426249, 703365119439919900]
8022 - [61870248763, 690781238]
8023 - [393128, 4389]
8024 - [638145, 7124]
8025 - [92449, 1032]
8026 [65969631962856149425205677574778384525, 736367281423878706277491995088206301] [8703984682629383388830651566720427067508276992383564028416176334337518951251, 97155757090044395992772334265217431200580686971360218475578459137411784050]
8027 - [4927635001, 54999900]
8028 - [100351, 1120]
8029 - [3385783259676816171808275303062455, 37785782851033186634997356320284]
8030 - [80789391, 901564]
8031 - [28568917490151799293036719754265, 318793143246035812202016820652]
8032 - [29373856534523897137, 327754844375795343]
8033 - [239977875293239401, 2677517514622940]
8034 - [229516474045, 2560636606]
8035 - [79752408702542412761606149846, 889714908846615094479511743]
8036 - [141012534067201, 1573032708480]
8037 - [74211160694084260001, 827793934806438600]
8038 - [35998633911942404805787021366431031084698342753068793054257477, 401524471743707255017105254231154165114776422969039603350434]
8039 - [9202956246192852862572460602152003722680, 102642292393302545710785612880538353171]
8040 - [269, 3]
8041 - [551753880430901373260365272535, 6153048879817054515744906108]
8042 [16284019901, 181584841] [530338608272328099603, 5913862329127841482]
8043 - [2370066047, 26427216]
8044 - [1049127427916158114806779733088568128160154415031312694153719134022041794584311295664199, 11697477276756106298580531544898675174704124109193200864610528573103529974871645783330]
8045 - [28827962091561670561, 321403734059764104]
8046 - [106922699, 1192010]
8047 - [4281972292766843542412, 47733892655201084913]
8048 - [1215047807, 13544076]
8049 - [29384215, 327524]
8050 - [134792099, 1502334]
8051 - [974170, 10857]
8052 - [152409599, 1698480]
8053 [247848755613676185222878383720685516593567518, 2761899638602950791016526403867324764335305] [122858011318495564675756140305745767199045322870429469342986534108128140667321948849360649, 1369066777115206654132033104494937885309464417792694615241794932122752485217643817245980]
8054 - [792788585774525308333644973053553439769932965, 8833881639981338811562878473513996198776434]
8055 - [359, 4]
8056 - [32379412473170124875, 360752405297545977]
8057 - [53948016863, 601019832]
8058 - [10853651, 120910]
8059 - [26183690, 291669]
8060 - [326431, 3636]
8061 - [473868069937009963824908981162759649891532897833225273448024032095, 5277922217441394752042979563775957154717855301336591757948031272]
8062 - [108532128436626167295157, 1208751213762802666302]
8063 - [1505045421276, 16761052135]
8064 - [449, 5]
8065 [89684999352603784209971640372, 998659927203289261517268073] [16086798217753082385728946705549210311593650113017000596769, 179129629849396679373243039111895966873963005783746886312]
8066 [334088391895, 3719908669] [223230107197974203382051, 2485556610444959675510]
8067 - [575088362, 6402927]
8068 - [22691017898615873418283839489716246568157231499338273, 252621921181419673667542341878442589909639500381564]
8069 [8838801470, 98397377] [156248822852148321801, 1739429760943488380]
8070 - [539, 6]
8071 - [3491118388403442731666372910200, 38859830585541551111317949763]
8072 - [56280003, 626417]
8073 - [859685399, 9568020]
8074 - [5056525, 56274]
8075 - [23274, 259]
8076 - [908551, 10110]
8077 [10297804554882, 114582845605] [212089557301096932300067849, 2359903498765019909987220]
8078 - [41735221263, 464355716]
8079 - [4001726295499740021498254681844676, 44521375855254254611642593508545]
8080 - [809, 9]
8081 [10477311488837249086213722320, 116551348379472898653809689] [219548112068242026166620113211043474700402552540132364801, 2442289562831448188755821759319738425621222675143116960]
8082 - [899, 10]
8083 - [120833, 1344]
8084 - [45495, 506]
8085 - [1079, 12]
8086 - [8154855953077956254238396174426966534720901199, 90687916757356045972841837945068483111472460]
8087 - [50693838991504585722813528, 563717425169005068946747]
8088 - [1349, 15]
8089 [126641737782008165258837170340376209400817701901770225529127780406079641019968, 1408086852982340981803046796940058181198420437615859315377579235666589143565] [32076259496893828809322316471266070148654593149136200536695448529769337299806944818314846478326298704169118033480008411183967565371763745972155086749442049, 356645132019365417375267406920617470524858106535305814634368386289280914662506195699925976709093190245182461194019659551746240219304305982326224367411840]
8090 - [1619, 18]
8091 - [1799, 20]
8092 - [8193151, 91080]
8093 [3658200499380129900586382, 40664246984092468494365] [26764861787330063570328689582658097324774887699849, 297515937248248018943421951605354455748325474860]
8094 - [2699, 30]
8095 - [3239, 36]
8096 - [4049, 45]
8097 - [5399, 60]
8098 - [8099, 90]
8099 - [90, 1]
8101 [90, 1] [16201, 180]
8102 - [8101, 90]
8103 - [5401, 60]
8104 - [4051, 45]
8105 - [3241, 36]
8106 - [2701, 30]
8107 - [4447205302565943872414162, 49392054613899601382493]
8108 - [8209351, 91170]
8109 - [1801, 20]
8110 - [1621, 18]
8111 - [73665054893515606412124479824991909281680, 817945403333110589603097853074493240903]
8112 - [1351, 15]
8113 - [119454103, 1326204]
8114 - [5281052793602273425, 58627720316008404]
8115 - [1081, 12]
8116 - [4164193801, 46223190]
8117 [36172524131861698469882, 401495832843659557945] [2616903004140233845105294735396161960122187849, 29046235404758372109879371905603062032624980]
8118 - [901, 10]
8119 - [571382543814047000, 6341262004930539]
8120 - [811, 9]
8121 - [178254022615, 1978037788]
8122 - [9452705911499189687186810789928084223, 104887722154292425617807595305199632]
8123 - [231470104621786802, 2568246360393531]
8124 - [913951, 10140]
8125 [30349818, 336701] [1842222905266249, 20437628140836]
8126 - [76457535, 848168]
8127 - [868325401, 9632020]
8128 - [44757606858751, 496449422400]
8129 - [35644719617059391303471973118950848359374999, 395345355514082901632650396093890229662500]
8130 - [541, 6]
8131 - [283997344895996809679489863280761145, 3149504979287788647346919204984748]
8132 - [61795078487, 685259718]
8133 - [24651130804172023868175398399, 273345205046472869947944480]
8134 - [66958810703625858716068818113824171201, 742430230404143399824974896520112440]
8135 - [2253941772888644, 24989865224331]
8136 - [451, 5]
8137 - [19801701329602917847793024076035096144368351, 219518106394159360951917385165345347285960]
8138 - [61328593, 679836]
8139 - [86869899170, 962905779]
8140 - [329671, 3654]
8141 - [120649499465961205879374521513469613671395301375, 1337170069876257268244031722326147364838876608]
8142 - [39883, 442]
8143 - [5040643378849029537415959430343024, 55859076988225381650069341017545]
8144 - [313201220822405001, 3470600010203675]
8145 - [361, 4]
8146 [298943650695, 3312204409] [178734612581708347966051, 1980324955749069828510]
8147 - [2496732527435961497282, 27661336579635610647]
8148 - [155143351, 1718730]
8149 - [609953023409225026049, 6756849247384323360]
8150 - [211249, 2340]
8151 - [693824, 7685]
8152 - [16073715125005882674057412962488837, 178026306454891414378830746462853]
8153 - [47006369499007, 520592598096]
8154 - [109082701, 1208010]
8155 - [3115372791330017126, 34498327435193115]
8156 - [64240368441700394665869043355904424659205507199, 711327198079400676938788187109282845275766760]
8157 - [101829512123810145205129279351, 1127478922759440738882690540]
8158 - [6489720113216811430207346862326543253025297456703, 71851215026237430172055421428888302355992366824]
8159 - [13260332938083360, 146803348543631]
8160 - [271, 3]
8161 [31302791045679731153820380678025366693404146527972412356878760, 346506489997697008672757941006987693314406719274386658310321] [1959729454498974313150188588189281879288568779983506998934101043493733322464503257589446831539831633239887089801378678275201, 21693240504739646499914558790920916035891700665550410175649427285982696784784408607441334663117019819794466485166107363920]
8162 - [2387967, 26432]
8163 - [123823410343073497682, 1370496285913769839]
8164 - [15380575814145385, 170224119628554]
8165 - [27831, 308]
8166 - [107123804060954138176318085, 1185444698229563030267858]
8167 - [8198336644815180496316602313424881726159402305357479697688, 90718209461064937249004952183265315706137090464439606227]
8168 - [10775075410899, 119223661055]
8169 - [72455865818587272592255, 801657947473454923536]
8170 - [7435899515789, 82266398334]
8171 - [3864599153648084310091261818312982318937627907970, 42753025041643745112192494173281521107491909987]
8172 - [102151, 1130]
8173 - [20256633986657580512351, 224066294219452156920]
8174 - [44683603828232752299, 494232016775003890]
8175 - [40872601, 452052]
8176 - [35087884780634163199, 388049159253616560]
8177 [177764644, 1965841] [63200537312893473, 698914051051208]
8178 - [2475415458751, 27373135400]
8179 - [79110694756024455833366950294757769472263659413353804728646410, 874752302794073994701313134370136377341929967807089533173559]
8180 - [33708961, 372708]
8181 - [2110134792407201, 23329584386680]
8182 - [129683393876550132825654183814801637, 1433687933650534917543559344218082]
8183 - [56447, 624]
8184 - [1668545, 18444]
8185 [26508, 293] [1405348129, 15533688]
8186 [787893824933355605, 8708268810955729] [1241553358736226420843439450769832051, 13722382444023507842139822138022090]
8187 - [153692204205247995556202, 1698593445719118343637]
8188 - [61965263913869969407, 684793117350442464]
8189 - [20057745683130380811128176956475068799, 221649463755589176870616993224414960]
8190 - [181, 2]
8191 - [137168708703221032895073625802589931406141894540466576152225731961377054107539335040, 1515606947046439809691055132298479939258772521204671748899078157656970867149893633]
8192 - [1572584048032918633353217, 17374763192966689655283]
8193 - [1886651874989012856218131710948511447, 20843483080810098101013521971548916]
8194 - [136333746755, 1506105486]
8195 - [1183359, 13072]
8196 - [28661728361680464688535, 316593067532762914738]
8197 - [146608600447, 1619317392]
8198 - [11275822732105182296718870099598277, 124535819426801659865055165281106]
8199 - [276518942427762746967306700799, 3053827094736687388602511040]
8200 - [17322499, 191295]
8201 - [603657110061089139407868444224654999, 6665871145831277093969547482963700]
8202 - [8048034309059327, 88864834550992]
8203 - [69876915611822519318, 771520323981133629]
8204 - [842285855887727892551, 9299223418951608870]
8205 - [13967080047943682561, 154193593372525728]
8206 - [3883082240888268907037646791150273761018548715, 42865790035152560479573862767830239322988398]
8207 - [5131424487, 56642932]
8208 - [13771351, 152005]
8209 [118329823595508562514842483613510842243706752894321294718305186200, 1306017779460169052797108690825691071967039014308898936872736633] [28003894304288349898723879892456670308002159346050114125214209143900753130515029037159170314667925467480257069104452243633340880001, 309081706912239220065422744851899850467070756449121475541005242263956175977884900275952471951526481109828540226232469741252129200]
8210 [2699153, 29789] [14570853834819, 160810137434]
8211 - [819790, 9047]
8212 - [250607337495961345281030961012407293763134459221296801448080649, 2765472295978832195584022177792054378016273988949721901631010]
8213 - [68823914119671440021808342521302399, 759431236896294225262419511793520]
8214 - [4122760103977442405, 45489453093011054]
8215 - [2266361120863317476044, 25004911824627069597]
8216 - [1877199, 20710]
8217 - [515734243080407, 5689437417188]
8218 - [153480897410013559693, 1693055759145414906]
8219 - [82444845786396915043900335392563051031893219250, 909398052399545914041796610664171558308623989]
8220 - [36991, 408]
8221 [178025853716887714711448906260262059047272461895876132512110, 1963454099273673447584694910468670246584525092974090573341] [63386409183253406694761352620008285420905508052868376131414908932433377487715199740268485883186297620551352358593304201, 699091184514237036237692381645834763568807198842708945177722630605641818887709050342199022173399693252717841051319020]
8222 - [1053349186343849850943743, 11616722843361036715472]
8223 - [2060086878724, 22718015465]
8224 - [4625, 51]
8225 - [11294696504449, 124539355056]
8226 - [7828332763526801, 86312744389060]
8227 - [510082226, 5623665]
8228 - [2177, 24]
8229 - [128022985, 1411284]
8230 - [127784903681868393771416411, 1408573885145201639851098]
8231 - [1839867157197208529161310660737560, 20279636496668249278595143508173]
8232 - [3974443213, 43804993]
8233 [1423428020455779671634691758607445333663405561354089760690868, 15687598042648387406031544493144234861549848218688422505165] [4052294658837319022620348031210510360722681564819754189408927150604158789191819041913864396868859249720024338201317186849, 44660333255105915852351465212070049548182348310662705898456130041915858633489565594695762990620087602692613379396666440]
8234 - [1185844375583572015, 13068395419552356]
8235 - [7085881, 78084]
8236 - [76292657571747809951, 840668112339474780]
8237 [4529004843823528156553518, 49902034506407808712565] [41023769750753961336867378092023567304023996352649, 452013111992339621355113094362544451886203107340]
8238 - [6557939976107, 72253109714]
8239 - [500210743040392735, 5510814131674296]
8240 - [605937671, 6675201]
8241 - [736443646618216125679618049, 8112403854861564353244480]
8242 [419340909993, 4619031545] [351693597587514654520099, 3873897782733345458370]
8243 - [45466393910829296491270735783204069726226, 500781019906570508443501201954122193095]
8244 - [5848201, 64410]
8245 [385673767362, 4247415721] [297488509662396192878089, 3276233645341310996004]
8246 - [3719071551, 40955560]
8247 - [10875338447581480807, 119755311315480828]
8248 - [567034525839383717427728783, 6243601511303111553790134]
8249 [94485341125220, 1040312420293] [17854959375098379631440096801, 196588547816374692364178920]
8250 - [246153932749, 2710065606]
8251 - [64402786498377807833127091852034385145, 709008374176384687747125409865960532]
8252 - [59951490401085766705151, 659964195156777766080]
8253 - [823604599, 9065940]
8254 - [577654334453292485851581892935964606486089828359307429976417734329459749819120785877550160558335, 6358223709236290061574010315726453921870012113456677129534822870715566661180788211955232206416]
8255 - [636, 7]
8256 - [568182049, 6253205]
8257 - [33314135970520991389756087460693566673709811622783, 366621062470581913364226823167916306496672142672]
8258 - [457232916099, 5031529790]
8259 - [368995411646138892497090, 4060291676333213153569]
8260 - [14475574716119, 159274331754]
8261 - [1050025119711312244192013695954290637791554999, 11552696860395191646854464481675014798389300]
8262 - [279921679351154808101, 3079597367060560010]
8263 - [483066902649541155343978350835010115224, 5314206257211653904943861797466397085]
8264 - [1930854760705, 21239997096]
8265 - [8567743529, 94242116]
8266 [6635658028395, 72985450981] [88063914939606037252552051, 968612987516204757210990]
8267 - [1182, 13]
8268 - [1273, 14]
8269 [4065871315935762332588829966711646431469032895832434047706621606979518277286976608918, 44712312629556291646366270108713307731912522429135709226183534514779781811876702645] [33062619115498415354672956090445328468427948652304945487550872739650291167548601953034995310740662490641188621406246998934867492994207172774777121423359925276149434261449, 363589018779330490688818677544195098479579467567926276302586281672943716849516060581657469634405970699780416915973273508806848984138038633877332234384105215179082376220]
8270 - [53071949502251, 583595972610]
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8999 - [85508363337533160, 901387368933299]


[参考文献]


Last Update: 2005.06.12
H.Nakao

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