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Integral Points on Conic Curves: x^2-Dy^2=±1(D \in [2000,2999])


[2003.08.16]x2-Dy2=±1 (D \in [2000,2999])の整点


2000≦D≦2999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
2000 - [930249, 20801]
2001 - [19742928095, 441354968]
2002 - [11325887, 253128]
2003 - [4344427204728362, 97071569134791]
2004 - [11242731902975, 251144109216]
2005 - [32724809, 730836]
2006 - [638145, 14248]
2007 - [224, 5]
2008 - [3832352837, 85523139]
2009 - [141012534067201, 3146065416960]
2010 - [269, 6]
2011 - [22903355954053525066202335319378237605968890, 510732021116138713675018566232201605320997]
2012 - [1215047807, 27088152]
2013 - [152409599, 3396960]
2014 - [32379412473170124875, 721504810595091954]
2015 - [404, 9]
2016 - [449, 10]
2017 [106515299132603184503844444, 2371696115380807559791481] [22691017898615873418283839489716246568157231499338273, 505243842362839347335084683756885179819279000763128]
2018 - [56280003, 1252834]
2019 - [674, 15]
2020 - [809, 18]
2021 - [45495, 1012]
2022 - [1349, 30]
2023 - [2024, 45]
2024 - [45, 1]
2026 [45, 1] [4051, 90]
2027 - [2026, 45]
2028 - [1351, 30]
2029 [45630, 1013] [4164193801, 92446380]
2030 - [811, 18]
2031 - [676, 15]
2032 - [44757606858751, 992898844800]
2033 - [61795078487, 1370519436]
2034 - [451, 10]
2035 - [406, 9]
2036 - [313201220822405001, 6941200020407350]
2037 - [155143351, 3437460]
2038 - [16073715125005882674057412962488837, 356052612909782828757661492925706]
2039 - [179221048487196942112440, 3968993620357130831179]
2040 - [271, 6]
2041 - [15380575814145385, 340448239257108]
2042 [2321107, 51365] [10775075410899, 238447322110]
2043 - [226, 5]
2044 - [35087884780634163199, 776098318507233120]
2045 - [33708961, 745416]
2046 - [1668545, 36888]
2047 - [5566204448, 123026943]
2048 - [886731088897, 19594173939]
2049 - [28661728361680464688535, 633186135065525829476]
2050 [2943, 65] [17322499, 382590]
2051 - [20521767174, 453139505]
2052 - [13771351, 304010]
2053 [11193912128830593631752403672482, 247051456555228090946659082305] [250607337495961345281030961012407293763134459221296801448080649, 5530944591957664391168044355584108756032547977899443803262020]
2054 - [1877199, 41420]
2055 - [136, 3]
2056 - [4625, 102]
2057 - [2177, 48]
2058 - [3974443213, 87609986]
2059 - [76292657571747809951, 1681336224678949560]
2060 - [605937671, 13350402]
2061 - [5848201, 128820]
2062 - [567034525839383717427728783, 12487203022606223107580268]
2063 - [173135049024, 3811846295]
2064 - [16855, 371]
2065 - [14475574716119, 318548663508]
2066 - [1930854760705, 42479994192]
2067 - [1273, 28]
2068 - [590968985399, 12995393130]
2069 [6567170, 144377] [86255443617801, 1896296606180]
2070 - [91, 2]
2071 - [3367541100844631060, 73998489635355363]
2072 - [2367, 52]
2073 - [39676910452570843351, 871441415914250980]
2074 [1246879395, 27379157] [3109416451351132051, 68277013431540030]
2075 - [2205226, 48411]
2076 - [441156441438751, 9682309261300]
2077 - [109506943, 2402832]
2078 - [13206606399, 289713320]
2079 - [1755676, 38505]
2080 - [84474001, 1852215]
2081 [4060, 89] [32967201, 722680]
2082 - [1529122817, 33512128]
2083 - [62445567158446396645849585981125626, 1368223292197435389350164213197825]
2084 - [32961431500035201, 722033266327160]
2085 - [1285471, 28152]
2086 - [4669990321339855, 102248943296628]
2087 - [120084010141224, 2628596697805]
2088 - [19603, 429]
2089 [4018318140, 87917453] [32293761348506119201, 706560592424994840]
2090 - [20481, 448]
2091 - [253010, 5533]
2092 - [13385850577032991983751, 292661188995551486550]
2093 - [183, 4]
2094 - [20080832545197365, 438827035407914]
2095 - [56227508629697854439, 1228448140439118324]
2096 - [225144199, 4917735]
2097 - [2300086406901705857, 50227890194279728]
2098 - [5456897, 119136]
2099 - [1530170, 33399]
2100 - [6049, 132]
2101 - [13751, 300]
2102 - [41966540404457957, 915349213910082]
2103 - [34348, 749]
2104 - [84056091546952933775, 1832509878662147766]
2105 - [16978089, 370052]
2106 - [562756526801, 12262848340]
2107 - [168867574226, 3678866235]
2108 - [557567, 12144]
2109 - [838444191076855, 18257271349044]
2110 - [71406802077926581, 1554527310090786]
2111 - [769864187548064400, 16755986469105247]
2112 - [1057, 23]
2113 [31189508522399852302368, 678513952720481289185] [1945570883737706036137311990847801980996814849, 42325033421885323238322401350399374136580160]
2114 - [2115, 46]
2115 - [46, 1]
2117 [46, 1] [4233, 92]
2118 - [2117, 46]
2119 - [185977771273124, 4040132054325]
2120 - [1059, 23]
2121 - [947004461801, 20562773460]
2122 [201554830358307, 4375427790625] [81248699281531826148007812499, 1763777212168887748250943750]
2123 - [62078642, 1347309]
2124 - [561799, 12190]
2125 [123476065138818, 2678571934021] [30492677324331251603220874249, 661479045208373412203854356]
2126 - [2846915971617054735, 61743752276468668]
2127 - [6365401, 138020]
2128 - [2588599, 56115]
2129 [693860937639464847832, 15037810507126585945] [962886001563834652798926337561605830200449, 20868298597038898618149766995762189842480]
2130 - [23999, 520]
2131 - [452144894661429530942871827090, 9794582001683535518729480823]
2132 - [74859849, 1621270]
2133 - [228151, 4940]
2134 - [9701, 210]
2135 - [7624, 165]
2136 - [3678725, 79597]
2137 [1152621332834462080850809368, 24933565795489475497866445] [2657071873810183629927660276844678125066814921353118849, 57477919679025668074133797385020454311793670837713520]
2138 [21131, 457] [893038323, 19313734]
2139 - [185, 4]
2140 - [5241052780831, 113295235548]
2141 [437120560084723918, 9446977923957565] [382148768097565465940572604562541449, 8258936562456706424027181945079340]
2142 - [11663, 252]
2143 - [20237054048, 437155761]
2144 - [42588211249, 919765275]
2145 - [28159, 608]
2146 [210236127543, 4538292565] [88398458648553126433699, 1908226109045577235590]
2147 - [19322, 417]
2148 - [192349463, 4150246]
2149 - [737004830625573318331838783974317934135, 15898352671473750671298540899829872724]
2150 - [216528049, 4669764]
2151 - [76759023628799, 1655042828320]
2152 - [9536081203, 205564827]
2153 [232, 5] [107649, 2320]
2154 - [818767969199, 17641600980]
2155 - [225634595102009, 4860512347644]
2156 - [31521799, 678870]
2157 - [82139999, 1768600]
2158 - [218981472870187, 4713913970514]
2159 - [28576, 615]
2160 - [119071, 2562]
2161 [72790107317645621301516122280468, 1565831322153656243947011679505] [10596799446628733252272832676133784715292720112612262977708598049, 227954059961791143233987331823126742246798584250769902674816680]
2162 - [93, 2]
2163 - [5767, 124]
2164 - [3707453360023867028800645599667005001, 79697934860635055038593569387598450]
2165 [247458022, 5318297] [122470945304304969, 2632110512057068]
2166 - [456335045, 9805158]
2167 - [44495093096796772, 955834416754893]
2168 - [4293183, 92204]
2169 - [10085143557001249, 216547068348200]
2170 - [559, 12]
2171 - [10467498023126, 224653389675]
2172 - [669337, 14362]
2173 [606, 13] [734473, 15756]
2174 - [6720269075233323408756735, 144130831594640199270976]
2175 - [87724, 1881]
2176 - [11995201, 257145]
2177 - [5599, 120]
2178 - [19601, 420]
2179 - [240603723898420099641751383966815800602410, 5154347913276724527274139160292653303441]
2180 - [1961, 42]
2181 - [6513116394236867715918693317815, 139463643378251489774926196748]
2182 - [21115315970951941617317, 452033073379115994678]
2183 - [1107372, 23701]
2184 - [701, 15]
2185 - [2501491975869079, 53514736760052]
2186 [11047458715, 236285629] [244092688119258902451, 5220711462650613470]
2187 - [1385331749802026, 29623024395005]
2188 - [51313727893789284875438776327, 1097008286311765583836380066]
2189 - [701284897131794999, 14988963610793700]
2190 - [18251, 390]
2191 - [2812922316995718320, 60094752360539433]
2192 - [6083073, 129928]
2193 - [29439864343, 628660956]
2194 - [360608130778278261905, 7698696570811675764]
2195 - [28764159, 613952]
2196 - [1766319049, 37692330]
2197 [86149711981264908618, 1837971620798254505] [14843545748909797093290079362183781339849, 316681451523016538870549220125463648180]
2198 - [42292347, 902086]
2199 - [678352095385, 14465803324]
2200 - [30580901, 651987]
2201 - [23072561163011325951, 491796897487589120]
2202 - [593219533, 12641738]
2203 - [8826151854096025892882, 188046020279289948171]
2204 - [140448799, 2991660]
2205 - [51841, 1104]
2206 - [879046987036219577199102482497977431003135, 18715840511342009929147489921762333395648]
2207 - [2208, 47]
2208 - [47, 1]
2210 [47, 1] [4419, 94]
2211 - [2210, 47]
2212 - [624635837407, 13281108852]
2213 [51982, 1105] [5404256649, 114880220]
2214 - [2801381440774085, 59536519034846]
2215 - [30409059868444, 646124379867]
2216 - [60756099699, 1290639665]
2217 - [33101760540247, 703020915868]
2218 [306679179, 6511837] [188104237664228083, 3994089649883646]
2219 - [2405842335, 51072664]
2220 - [6581191, 139678]
2221 [5615331049782, 119151931205] [63063885597291636324495049, 1338155077873850588494620]
2222 - [9899, 210]
2223 - [85292, 1809]
2224 - [12032115501124999, 255137679217125]
2225 - [500001, 10600]
2226 - [48799645, 1034318]
2227 - [255171482138190122, 5407194947981673]
2228 - [27849, 590]
2229 - [6746130544160303087615, 142889299355407689216]
2230 - [72251, 1530]
2231 - [147355320, 3119723]
2232 - [7937, 168]
2233 - [10207, 216]
2234 [1726627468307, 36530621525] [5962484828624480578892499, 126149549118783899016350]
2235 - [626546, 13253]
2236 - [506568295, 10712778]
2237 [993983040438563518, 21015802691152685] [1976004569358981995803614798641072649, 41778702912417782604576378017491660]
2238 - [252149, 5330]
2239 - [125056611057426103817571970427014880, 2642893170294320623381279806789729]
2240 - [10081, 213]
2241 - [8553815, 180692]
2242 - [8130355506858257, 171708475260588]
2243 - [4216034762, 89020401]
2244 - [522785, 11036]
2245 - [3881607656256161, 81922550194296]
2246 - [105964274723956380485, 2235911419162860462]
2247 - [18724, 395]
2248 - [220938497, 4659864]
2249 [197140, 4157] [77728359201, 1639021960]
2250 - [39480499, 832322]
2251 - [182330, 3843]
2252 - [9281213767, 195578262]
2253 - [32049873888048012151, 675220670884419660]
2254 - [57643991108495, 1214163258516]
2255 - [3609, 76]
2256 - [95, 2]
2257 [49699491432, 1046131225] [4940078897198882821249, 103984379707270328400]
2258 [34831, 733] [2426397123, 51062246]
2259 - [3674890, 77319]
2260 - [435259412378569, 9155750551974]
2261 - [951, 20]
2262 - [97499, 2050]
2263 - [110888, 2331]
2264 - [95609285, 2009379]
2265 - [486976309471, 10232310984]
2266 - [2764743626523751885, 58079773336224042]
2267 - [11121951531682, 233590533237]
2268 - [8193151, 172040]
2269 [122519087946282, 2572092051085] [30021853822377566529035247049, 630260744425631939359631940]
2270 - [24618466891, 516711438]
2271 - [2737623170905, 57446701988]
2272 - [143, 3]
2273 [618833632, 12979985] [765910128188622849, 16064902521711040]
2274 - [22036808705, 462118624]
2275 - [1574, 33]
2276 - [16760473211643448449, 351317794262007160]
2277 - [3222617399, 67534740]
2278 - [14945957, 313146]
2279 - [181556905575, 3803125084]
2280 - [191, 4]
2281 [38611201941558710493130588671468, 808445370637135345218841693805] [2981649830743654269669907724743299862819650512057127554474550049, 62430094928777423119382521794712492545154361356761603591711480]
2282 - [3570351, 74740]
2283 - [79834226, 1670845]
2284 - [65612063992983395551353492198003600753799, 1372889710241988479048470561798891118310]
2285 [6826318, 142805] [93197234874249, 1949664683980]
2286 - [130049, 2720]
2287 - [3408802706371217226890624, 71280179337004908750375]
2288 - [287, 6]
2289 - [2883049, 60260]
2290 [42483057, 887765] [3609620264130499, 75429942195210]
2291 - [82926027861510, 1732520247017]
2292 - [383, 8]
2293 [44704115075962513571096979373518, 933566964054374671074594187945] [3996915809449797781026127104343692038269891422048887887519392649, 83468569984407449450628148057917020621955697123575980095681020]
2294 - [3294555, 68786]
2295 - [16336, 341]
2296 - [575, 12]
2297 [440130758627351632, 9183351821115805] [387430169379776126085928364346126849, 8083751207539140825274724655487520]
2298 - [767, 16]
2299 - [19651490, 409851]
2300 - [1151, 24]
2301 - [1535, 32]
2302 - [2303, 48]
2303 - [48, 1]
2305 [48, 1] [4609, 96]
2306 - [2305, 48]
2307 - [1537, 32]
2308 - [1153, 24]
2309 [2697643107218, 56140015265] [14554556667841571687399049, 302891450437481103365540]
2310 - [769, 16]
2311 - [400892050972310899724010277137604913515533179720, 8339259190601108963913338322963746423187510147]
2312 - [577, 12]
2313 - [526337, 10944]
2314 [376264473957, 7821887005] [283149908724275862475699, 5886196398574838457570]
2315 - [131533206, 2733757]
2316 - [385, 8]
2317 - [837558013263245527053151, 17400105486629221264920]
2318 - [2588597, 53766]
2319 - [11248310441088076, 233580680620735]
2320 - [289, 6]
2321 - [418350700413556946199, 8683662388409533340]
2322 - [67897601, 1409040]
2323 - [32130633887, 666645096]
2324 - [152071153975, 3154487274]
2325 - [12151, 252]
2326 - [1011704154316301042971871388557808298433676201125, 20977255994808703605657308111046802217613857982]
2327 - [9050599, 187620]
2328 - [193, 4]
2329 - [1070304336185345, 22178008247616]
2330 [6613, 137] [87463539, 1811962]
2331 - [847225, 17548]
2332 - [8429543, 174558]
2333 [21819558722870482, 451740048139805] [952186285721586679031291493824649, 19713537015717627287428087472020]
2334 - [1074126251, 22233350]
2335 - [4204, 87]
2336 - [145, 3]
2337 - [672604673, 13913312]
2338 - [675683, 13974]
2339 - [6959111461257844826290, 143892673428943412721]
2340 - [33281, 688]
2341 [8648611541418, 178749849185] [149596963188697267858901449, 3091876017376235762088660]
2342 - [251103639062501, 5188711946250]
2343 - [10649, 220]
2344 - [33867877212256207699, 699534556029004155]
2345 - [15129001, 312420]
2346 - [46622195, 962562]
2347 - [323870477352338993274741120507602, 6685206343255953671339194057443]
2348 - [7274533788487, 150126071154]
2349 - [192119201, 3963960]
2350 - [9187426914049, 189522146352]
2351 - [5381836320, 110995193]
2352 - [97, 2]
2353 - [28426024561897, 586010183844]
2354 - [26851797424385, 553439475216]
2355 - [45374, 935]
2356 - [41423166067036218751, 853405911531873000]
2357 [25294, 521] [1279572873, 26356348]
2358 - [104980517, 2161906]
2359 - [8127739376, 167342325]
2360 - [5781, 119]
2361 - [272492068098280169294544535, 5607972450814722925722772]
2362 [243, 5] [118099, 2430]
2363 - [1070271226, 22017195]
2364 - [54897073951, 1129081940]
2365 - [155231, 3192]
2366 - [362074049, 7443720]
2367 - [38713200767, 795719408]
2368 - [10657, 219]
2369 - [4796828434236403935, 98553409885410536]
2370 - [4406461, 90514]
2371 - [191040489782439912520686852440210, 3923373423465515100422422137087]
2372 - [721517598849, 14814588280]
2373 - [19825399, 406980]
2374 - [47541174557527728086227215574494403891385765, 975729756992818394465954368763068733505174]
2375 - [1442400999, 29597444]
2376 - [1098305, 22532]
2377 [26940448820615587038280339176, 552573732045165317517403349] [1451575565312415549196945328336473408820113982859200717953, 29773168695558654784315702895565504921917594965036600848]
2378 [829, 17] [1374483, 28186]
2379 - [1951, 40]
2380 - [685536391, 14052126]
2381 [75484224514275122210050582, 1546950794978232497464885] [11395736301042986619081135380398394825126509997077449, 233540762241346572206168462525797675029565237626140]
2382 - [1135209064373, 23259746202]
2383 - [19515644377863617024, 399779825830543095]
2384 - [25801741449, 528440255]
2385 - [73738369, 1509904]
2386 - [341500494791825, 6991270689972]
2387 - [342, 7]
2388 - [463287093751, 9480539250]
2389 [12376139172165997847649094782650519444842530, 253207817312059057021841082272711737615897] [306337641617643341027085710770455942914371640417170871093925283234950306862032993601801, 6267470373068851592534232163240483565084111376077086357718810651845698044589579398820]
2390 - [38719, 792]
2391 - [148084286735433124, 3028441506476925]
2392 - [1574351, 32190]
2393 [384224677924, 7854416117] [295257206251603065899553, 6035721005670799402216]
2394 - [685, 14]
2395 - [103771570282402499999, 2120438249781879000]
2396 - [1218834694718570634844060799, 24900117775077576036296520]
2397 - [58751, 1200]
2398 - [47758341060857899, 975269501660730]
2399 - [2400, 49]
2400 - [49, 1]
2402 [49, 1] [4803, 98]
2403 - [2402, 49]
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2998 - [27672421205427535850325684101, 505395470410258019579528970]
2999 - [416116196387217480, 7598474094718699]


[参考文献]


Last Update: 2005.06.12
H.Nakao

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