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Integral Points on Conic Curves: x^2-Dy^2=±1(D \in [6000,6999])


[2003.08.16]x2-Dy2=±1 (D \in [6000,6999])の整点


6000≦D≦6999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
6000 - [457470751, 5905922]
6001 - [427383235354625, 5517034109568]
6002 [334759, 4321] [224127176163, 2892987278]
6003 - [107119097, 1382556]
6004 - [13534735238019723614555987551, 174674465453009495303125380]
6005 - [9609, 124]
6006 - [155, 2]
6007 - [212944959637635956041411259275470084748807993181498024, 2747505363507560917730595352460848591609976038952565]
6008 - [5966017599, 76969660]
6009 - [131634010632725315892594469510599473884013975, 1698114661157803451688949237883146576681644]
6010 [352581333, 4548017] [248627192760113779, 3207091792733322]
6011 - [9539196490076155387105860370, 123037764169347298383022053]
6012 - [56447, 728]
6013 - [40929908599, 527831340]
6014 - [1551, 20]
6015 - [342735471124, 4419175385]
6016 - [2143295, 27633]
6017 - [38663097270385396036887, 498432825756361350652]
6018 - [6553601, 84480]
6019 - [44518093679954899843280092574, 573818290593150914888394495]
6020 - [11968361, 154254]
6021 - [14226117859054135, 183337830872812]
6022 - [14481399590265759857483754115040053767681416211227684896901, 186612255380004919276513683556553546068825842715970107230]
6023 - [691544692, 8910741]
6024 - [31880816705, 410758876]
6025 [71011068, 914845] [10085143557001249, 129928241008920]
6026 - [33535, 432]
6027 - [7263026, 93555]
6028 - [47898126226567, 616924336014]
6029 [767027328119637288473301125075158071704582, 9878436115934112202852491783544399438645] [1176661844164699446855991606809656920162182488742587760188198784503702178918159589449, 15154060920010939236546452898331365986461860697788147121249615892240642198148742780]
6030 - [5791211, 74578]
6031 - [26787050250659946106608240002213485498124, 344929412066876913873610602177035825025]
6032 - [233, 3]
6033 - [307692245718165012682196091607, 3961410869554194275790454484]
6034 - [6090617606629949, 78407693893830]
6035 - [22365354, 287897]
6036 - [64393055, 828828]
6037 [48190946221007058398721277970315764818, 620232994644366193883579311390008025] [4644734595351988965334734026985501244007860378347965024883897252680573146249, 59779229778801620243700643861476444073820455805708055902010680922065328900]
6038 - [4008116056727216197, 51581472270403446]
6039 - [6872608799, 88438040]
6040 - [84053391679, 1081525524]
6041 - [183206264437650472890152233695, 2357142843621055006313324408]
6042 - [25651, 330]
6043 - [36598002280524519467536831548019441595970530330795126762, 470794177103243661941228806348455704042512834936453851]
6044 - [2958302061967678577584535205763199, 38052245359198029920180065571880]
6045 - [311, 4]
6046 - [5132193613765015388397879165456873963975883745449535, 66003803167785047994832804327094707667213145573912]
6047 - [64753195081968, 832705087697]
6048 - [153090001, 1968525]
6049 - [243294493679774598512720680445363836180235698169324358151705055, 3128171015510663971098433869510378055844525997455385470444424]
6050 - [19601, 252]
6051 - [16671765626, 214322625]
6052 - [22280499233, 286401612]
6053 [29432518, 378305] [1732546231640649, 22268937443980]
6054 - [50793643201, 652812040]
6055 - [432517393974464, 5558357855187]
6056 - [5151268521999699, 66194400893635]
6057 - [4765506835465395993032041249, 61232262965529140566344200]
6058 - [467, 6]
6059 - [4197089314646034408890, 53919733238089469331]
6060 - [512071, 6578]
6061 - [157597811024093244767760299820449, 2024314747332761135364428454840]
6062 - [307914009999, 3954772300]
6063 - [193028, 2479]
6064 - [334949171001860160500111891352199, 4301295809286972312536199381645]
6065 [15112184446328, 194049193897] [456756237479675839825367169, 5865014419665459323320432]
6066 - [911249, 11700]
6067 - [127309075488718166993535420463236227064395992442, 1634452737486867684253105113355551170350915017]
6068 - [29601, 380]
6069 - [10710859270003201, 137488300736160]
6070 - [5109545835426464619070275212078684411, 65582497871547156843875928512634966]
6071 - [935, 12]
6072 - [1013, 13]
6073 [10001741013316352172059338328609382222297029594016, 128343525276492093170892185079171874167498932797] [200069646594908822313550224717114640121925889131069984935171772818613045765173365093650619566016513, 2567317401102989772057000899601442274058352047967834550491807836281253595735845161849612354685504]
6074 [152048734925, 1950946757] [46237635584585829511251, 593277972615762776450]
6075 - [70226, 901]
6076 - [4620799, 59280]
6077 - [7273774583252527786586031089151, 93307213466620364159205128480]
6078 - [2027, 26]
6079 - [15683834402554365557051061670634704683680, 201157475419668779582887925165496393759]
6080 - [3041, 39]
6081 - [4055, 52]
6082 - [6083, 78]
6083 - [78, 1]
6085 [78, 1] [12169, 156]
6086 - [6085, 78]
6087 - [4057, 52]
6088 - [3043, 39]
6089 [1472027248808210684061068, 18864394166205944139325] [4333728442467739605556854587584374952209506601249, 55537804489827590932238469896503028290000598200]
6090 - [2029, 26]
6091 - [584616962716824808350648037352058628366388060408472879488221610, 7490781212129546255272727658542701332416923599329414071554717]
6092 - [4632967, 59358]
6093 - [3661217, 46904]
6094 - [4636969901533241220474605648381999463595, 59399535927059638100759617924713265314]
6095 - [1335864, 17111]
6096 - [1015, 13]
6097 - [937, 12]
6098 - [1691924547601, 21666426180]
6099 - [8448826, 108185]
6100 - [1766319049, 22615398]
6101 [8255990709247543100915768299182716629418, 105698465663087350033891508825157299785] [136322765182363499527073085052218951639742148028494742852951311613259749486037449, 1745291100992339224175037268598346117312624883813344453779931317230746752150260]
6102 - [1241152901, 15888730]
6103 - [14719270328, 188414619]
6104 - [102135615, 1307284]
6105 - [3051350039, 39052532]
6106 - [14895447275735218328085643859262843130799, 190622933497020383651156507812039332420]
6107 - [1879758438, 24054043]
6108 - [516127, 6604]
6109 [178087794584121342044413162830, 2278500315912074998809502333] [63430525159672397614431445235362621182841529505128187217801, 811546192440010393759435009139775467978778738533587764780]
6110 - [469, 6]
6111 - [17792625320, 227606097]
6112 - [164998439999, 2110513650]
6113 [29476, 377] [1737669153, 22224904]
6114 - [1711679856314881425425, 21890708736096655596]
6115 - [99391628589911843751064846, 1271017634523543992547921]
6116 - [72285400494999, 924308300650]
6117 - [542965240056254939999, 6942290571784470600]
6118 - [2732353217, 34932696]
6119 - [1844554214659749285096820, 23580401626685749945989]
6120 - [229841, 2938]
6121 [14314112001930713375821395383369918970265734338836704468, 182958765531005524314421118762946847371585077860875245] [409787604807633790013077490334511127747925165619294104547480126994384467055608333313661792761022637469542326049, 5237784523091586966979659874970181163735077190289465592191806359186428246339300139294510160437970019764189320]
6122 [32588604590149, 416503928629] [2124034298266160944535684403, 27146563680668241784951442]
6123 - [313, 4]
6124 - [2677624306214429786475249638342580072972656656831966368004999, 34216221657259933431900050388049918234334563910850140638650]
6125 - [5990827771012465337616001, 76547989357013809155312]
6126 - [3355083122065362228230645, 42866180469065661968282]
6127 - [5866027417279882751825730772, 74941114645556708866329423]
6128 - [704475647, 8999256]
6129 - [4959716478711767526219195477182007983255, 63352249473328844722466765458602620484]
6130 [32418948777, 414065161] [2101976479611499591459, 26847114489598516194]
6131 - [49614210577604002411363130, 633636851803875450384873]
6132 - [65935351, 842010]
6133 [2731793187344382, 34882799786185] [14925388036842355543538933923849, 190585189622796496155121925340]
6134 - [72077015807655696290322017106085, 920290441932190156995579791694]
6135 - [11044, 141]
6136 - [235, 3]
6137 - [11856808685922849, 151352552925080]
6138 - [1197901, 15290]
6139 - [8161297179501312283377727560663490105, 104162255528621864250418343097394404]
6140 - [3798451518751, 48475511700]
6141 - [16167915925315906726189413449, 206316752603451214753512540]
6142 - [10855911535790889583349, 138519651286016082930]
6143 - [1771432191312465554139780768, 22601344494970125265528319]
6144 - [4250272665676801, 54223954680245]
6145 [167313719352, 2134374433] [55987761366799638599809, 714220249750092254832]
6146 - [21951, 280]
6147 - [170067682, 2169153]
6148 - [75080329577, 957545106]
6149 - [35286500539575, 449993606924]
6150 - [15772656049, 201125564]
6151 - [301400, 3843]
6152 - [813603, 10373]
6153 - [677417, 8636]
6154 [126154012605777488235, 1608134328433752437] [31829669793077330814444925784611126830451, 405745196682030240730808673763340157390]
6155 - [2320108056249, 29572918300]
6156 - [772362118440199, 9844001234210]
6157 - [815264351, 10389960]
6158 - [5075004487342753030013583, 64672044148461439755956]
6159 - [89798097859458535, 1144226588567244]
6160 - [95831, 1221]
6161 [19151859799050559532, 243997484747895745] [733587467524977877075473328804552118049, 9346011238425353134293372003703982680]
6162 - [157, 2]
6163 - [83397229794190674424905673246189604754380876487122, 1062320448017609101225638765177440870561068218729]
6164 - [832350906580405815, 10601690996867446]
6165 - [95592800063517769, 1217471048564628]
6166 - [379150007900894070048371385161691610015246944721752485, 4828467462477747542138982725534349033416424643488642]
6167 - [486952488, 6200827]
6168 - [2592101, 33005]
6169 - [20943152339520598285001518255563059994856780470319537150843945951, 266645750424078250373531634667657730081712979043387694532083240]
6170 [427387, 5441] [365319295539, 4650825334]
6171 - [499850, 6363]
6172 - [88264614502614617052305990143716836545057454960767, 1123501534867158261758265602236306739772544209048]
6173 [2648239861326338318618, 33706152377609993165] [14026348726235487216356617524788846570859849, 178523952596652633810963796527641144491940]
6174 - [235451028081583642049, 2996520674982912040]
6175 - [2481903468612476, 31583947205097]
6176 - [24889036049, 316704645]
6177 - [6525587423, 83029192]
6178 [393, 5] [308899, 3930]
6179 - [30293545538926, 385381629105]
6180 - [123481961, 1570758]
6181 - [2448406505723004415, 31142548753561248]
6182 - [6397409076101, 81365373390]
6183 - [18078822919215001, 229916705428900]
6184 - [3802792051, 48357945]
6185 [90992, 1157] [16559088129, 210555488]
6186 - [3254645904366481171199, 41380790971543434960]
6187 - [46672332255537364215737, 593361611470807460892]
6188 - [27847, 354]
6189 - [230254182167960477557696338679978746829817962599568895, 2926828570592163323367101658955533509659800723993504]
6190 - [9915583260544301650076284501, 126029711216583522294269010]
6191 - [17234808349025280, 219041324258183]
6192 - [24248647, 308157]
6193 - [119489548766013461836908956026006487, 1518376176763202272759422673186476]
6194 - [364101214465, 4626329136]
6195 - [1889, 24]
6196 - [48106848972197087743588687481413975084698632248110750633952591202305801, 611154771413373747967121341673190254409038131589340983049336413981610]
6197 [411302117843667935840525208982, 5224806339157332388758237785] [338338864285373011648463943315481180498114822548469546952649, 4297947825236864773784575797605731414297158113422347569740]
6198 - [749957, 9526]
6199 - [1334715939069756049112164301351061316353993526339669270188099069560, 16952276551310688291810390609530011908356554225346673453494921301]
6200 - [999999, 12700]
6201 - [22049, 280]
6202 - [28351, 360]
6203 - [3859855934738054800202, 49008363963119005899]
6204 - [1850201, 23490]
6205 [51438, 653] [5291735689, 67178028]
6206 - [6214143846571125, 78881546510798]
6207 - [1077326942787724, 13674348642745]
6208 - [62809633, 797169]
6209 - [49850466175, 632642544]
6210 - [12732036031, 161566776]
6211 - [3015307160297076162906862907034791388714328650868600535105832229059981707210, 38260513493169948116680394654405444777600332690259618445124304827582603953]
6212 - [16865536001301633, 213985538734232]
6213 - [15921847, 201996]
6214 - [288397076776131137430295489915, 3658518281701470630626009346]
6215 - [40679, 516]
6216 - [160285, 2033]
6217 [17675746078656625646660459790829633304486710776, 224175073273328747156900399692276443205613141] [624863998874290156963553658261438898971951176856621596712434424251457866869214910374949044353, 7924923344687204654032982671345957119921034455665669162928413888146159200785543526823814832]
6218 [12217615146998989, 154939118912377] [298540239760358255182345534044243, 3785973052173069515050397173706]
6219 - [31138100617500578690, 394849724430336461]
6220 - [5117847907209209, 64892152926738]
6221 [2172250, 27541] [9437340125001, 119651874500]
6222 - [228751, 2900]
6223 - [423462818377139450624, 5368035548323545975]
6224 - [3287049, 41665]
6225 - [146335502108449, 1854727127976]
6226 - [71743590216577698156377901381185, 909240030403725577965040035768]
6227 - [57338925398, 726624633]
6228 - [12498490045601, 158373766980]
6229 [2877695879624850282, 36461600601832585] [16562267151219681608794427261830959049, 209850795632841182241287350908077940]
6230 - [100679291, 1275546]
6231 - [216865008288025, 2747328601948]
6232 - [17873016101, 226404015]
6233 - [703187492187007, 8906817910416]
6234 - [37047239444778205549, 469215611525502110]
6235 - [842884282106, 10674553701]
6236 - [9011163287820287809974698755199, 114111077486337980223673981560]
6237 - [246401, 3120]
6238 - [373679757813294143, 4731260793382536]
6239 - [6240, 79]
6240 - [79, 1]
6242 [79, 1] [12483, 158]
6243 - [6242, 79]
6244 - [171407516109350655091252735, 2169194099088947390803536]
6245 [246638, 3121] [121660606089, 1539514396]
6246 - [38782105445014642382885, 490716196967999224038]
6247 - [472990987601268762665254328, 5984351751020836092151917]
6248 - [1813197, 22939]
6249 - [9825613075160880188378315464235980879813015, 124295210914808012291559063589319946422924]
6250 [27701390939331835443, 350397958892159281] [1534734119947391816778057233430462012499, 19413021687231260093506860646474392966]
6251 - [157985799, 1998220]
6252 - [1157233998067025737351, 14635639363706794810]
6253 [18798954, 237733] [706801342988233, 8938263462564]
6254 - [3746403415701, 47373514210]
6255 - [2263164641, 28615576]
6256 - [107712448284799, 1361813162220]
6257 [46232087032756928233143868, 584467573778504374983505] [4274811742808822625855887050112739699582142372002849, 54042311477504190725960426710501119422433583794680]
6258 - [15464413, 195486]
6259 - [14517796173821068008744161427813650, 183505133895319752211176084276519]
6260 - [467897169491706249, 5913753953084950]
6261 - [1191956751986345380763135, 15063942393098505628128]
6262 - [44890941102353868470062264399, 567286147221108345450526740]
6263 - [108233539338317555156568, 1367636411104087212811]
6264 - [12219743051, 154396055]
6265 - [45934935575233872692281751, 580340091597629090340780]
6266 [14310275, 180781] [409567941151251, 5174051649550]
6267 - [33396842, 421867]
6268 - [13877260640767, 175282779504]
6269 [2419331186085704464831120190199159932381282, 30555978007372914008575627579303334177165] [11706326775933723130196167708436294136710656903175239633215194350466553637062047927049, 147850061029172425070313322277124868598392219998067126676175955076278782429035651060]
6270 - [4751, 60]
6271 - [112541601484424892497933143391522608020098227154361416284389842240, 1421165612812202524166316375074159976643924038940711078989749313]
6272 - [768398401, 9702495]
6273 - [34849, 440]
6274 [6807111135, 85939057] [92673524008481976451, 1169993423672199390]
6275 - [27009633024199, 340966583892]
6276 - [3674077401859095458455, 46377446585176975118]
6277 [840642369513307534050924052997118, 10610484393738596781432182464705] [1413359186841896568327437099229196415036298317095354565517032611849, 17839245484872768688629396208117996819922585654568440999003440380]
6278 - [253637477, 3201126]
6279 - [560624, 7075]
6280 - [287696384061859, 3630400861389]
6281 - [36123682081348270942190135049393036951, 455803457043368880208418036330490380]
6282 - [5407917424315217, 68230897746028]
6283 - [239890624591698648666937, 3026423811987555400764]
6284 - [4090168362623304347424199, 51596839105066183937430]
6285 - [4328398348919, 54597729396]
6286 - [152176931429797135, 1919382956919972]
6287 - [65933798103564121729904928, 831546162624805078518697]
6288 - [46437143, 585611]
6289 - [1109118954184074199, 13985800527625620]
6290 - [3331, 42]
6291 - [2271050, 28633]
6292 - [842401, 10620]
6293 - [16183, 204]
6294 - [56645, 714]
6295 - [70427183529913071748860084925997159, 887651422825520745400622769458172]
6296 - [3097184950960165, 39033256070787]
6297 - [5356961766988548881976326916423383, 67507449489205038535285979185252]
6298 - [763026050144692493, 9614750903254374]
6299 - [600135910999715084435810, 7561601928784324456149]
6300 - [8193151, 103224]
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6970 [114627, 1373] [26278698259, 314765742]
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6986 - [2801206037318655, 33514347085472]
6987 - [2019242, 24157]
6988 - [1044569290011071836455833392478955577564317700186803847, 12495706198044240850298425769101957321286983296906846]
6989 [418, 5] [349449, 4180]
6990 - [18427780800271, 220411601316]
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6992 - [4599, 55]
6993 - [44357599, 530440]
6994 [6105, 73] [74542051, 891330]
6995 - [338559, 4048]
6996 - [31356358199, 374887290]
6997 [24430434380010161118, 292062132544180505] [1193692247991964930906105953856638019849, 14270409528012863912139749916649209180]
6998 - [16246391210119762757, 194209261890019926]
6999 - [38207774628414076, 456702876147965]


[参考文献]


Last Update: 2005.06.12
H.Nakao

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