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Integral Points on Conic Curves: x^2-Dy^2=±1(D \in [5000,5999])


[2003.08.16]x2-Dy2=±1 (D \in [5000,5999])の整点


5000≦D≦5999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
5000 - [152139002499, 2151570407]
5001 - [3509480115496136587702226332407575, 49626581352106209709036040453932]
5002 - [390401, 5520]
5003 - [48423659490675226, 684608608130205]
5004 - [12032115501124999, 170091786144750]
5005 - [44268809311, 625742712]
5006 - [48158641949558952251442749803488001841295, 680657773686093065717523633838561099252]
5007 - [217034724223897, 3067188224212]
5008 - [32188120829134849, 454845039641040]
5009 [19425271786026179421847070432797420, 274467918059139017587150815234817] [754682367921969429130320127864154620855710960099814496864813517312801, 10663227809687076898395591777372183513500019124430822841430983544280]
5010 - [684031, 9664]
5011 - [1576004487359930, 22263592706553]
5012 - [2772351, 39160]
5013 - [1551133601, 21907880]
5014 - [25157598731408198132266996072608016699, 355285121749346859670064114879166870]
5015 - [4249, 60]
5016 - [362405, 5117]
5017 - [74400254699619404393, 1050394337273772012]
5018 [2621, 37] [13739283, 193954]
5019 - [109115136670, 1540197461]
5020 - [31134002572889, 439423317354]
5021 [1511264299210, 21327763309] [4567839564133384813248201, 64463774541785271371780]
5022 - [7937, 112]
5023 - [262651211423970166717203799863486758357432343008, 3705935182493393334207534987381977802152854191]
5024 - [308110930001, 4346926425]
5025 - [530645718049, 7485772616]
5026 - [1043204847875, 14714935218]
5027 - [1392425960122, 19638923073]
5028 - [101399, 1430]
5029 - [91059678760321912033649473475404820231735, 1284059936934832497698286520584540355116]
5030 - [25697199246840251, 362327918745090]
5031 - [506568295, 7141852]
5032 - [26297959123, 370724877]
5033 - [1237553622314329823, 17444180045659704]
5034 - [646660663843591585199, 9114226940885505620]
5035 - [2788140475126, 39292975155]
5036 - [24823994659119492914464992199, 349807251713098296774073890]
5037 - [178849, 2520]
5038 - [41471811002357, 584283899514]
5039 - [5040, 71]
5040 - [71, 1]
5042 [71, 1] [10083, 142]
5043 - [5042, 71]
5044 - [121645306092343879707029626249, 1712804583974085402545439450]
5045 [179062, 2521] [64126399689, 902830604]
5046 - [43374646022449, 610607761660]
5047 - [103537981567, 1457414352]
5048 - [61855669263, 870602354]
5049 - [571517253246778145, 8043159114923576]
5050 [123954938307, 1744287805] [30729653461384352052499, 432426174516854892270]
5051 - [19888215137098831204331127274450, 279838281401562462581280432507]
5052 - [142297, 2002]
5053 - [193399882066783, 2720705633064]
5054 - [291977237261249, 4107063107400]
5055 - [69437164, 976633]
5056 - [12799, 180]
5057 - [17739177, 249452]
5058 - [220938497, 3106576]
5059 - [7861175388095683510993718096242134014475170, 110523631471908096357595246913049265441569]
5060 - [206999, 2910]
5061 - [149084904533566230391735, 2095634323233091498572]
5062 - [13269138833223402948205313366431815596559557, 186501215950563142121888562911191933679502]
5063 - [5977, 84]
5064 - [533240465, 7493354]
5065 [31634087501444365934662008, 444493676268463055914901] [2001430984098077293440641361897224111925818397184129, 28122303697830490651008442867955305796205291562416]
5066 - [4935475, 69342]
5067 - [68122, 957]
5068 - [782536684342298887, 10992245081062674]
5069 - [1193545, 16764]
5070 - [55989361, 786324]
5071 - [166420, 2337]
5072 - [248678907849, 3491799745]
5073 - [2849, 40]
5074 - [6948610614585441764473593889025, 97548982544630385341332460976]
5075 - [740601, 10396]
5076 - [3429215, 48132]
5077 [830220424818, 11651714425] [1378531907569960780666249, 19346982599563037199300]
5078 - [36875592335194597, 517478912598894]
5079 - [10822950672347972917163815, 151864607719463265694484]
5080 - [581837113691, 8163371559]
5081 [25651300, 359861] [1315978383380001, 18461804938600]
5082 - [5896813, 82718]
5083 - [302685827833, 4245531156]
5084 - [32799, 460]
5085 - [435259412378569, 6103833701316]
5086 - [40649747826366232986892420951279873477215591314529966345408399116353535, 569993204274597143628517250407924455081205201430994479312401162860672]
5087 - [16889796629026050624, 236806463164818575]
5088 - [22897, 321]
5089 - [20546679098158975, 288021834790896]
5090 [133057, 1865] [35408330499, 496302610]
5091 - [2524438349549261172844610, 35380439261774551863217]
5092 - [183449440868134807, 2570823107925738]
5093 - [406622115495251103769399, 5697760070699198771220]
5094 - [95609285, 1339586]
5095 - [1713959, 24012]
5096 - [54100801, 757860]
5097 - [4695585219038687111593292068056151, 65770691817474628845006669093220]
5098 [357, 5] [254899, 3570]
5099 - [11214174610, 157045251]
5100 - [4999, 70]
5101 [2719816819724124619551159733040372664335849827710, 38081319968893806997562134652020942285407344501] [14794807065708502800277594820795245963345503675626759321673519927486108806939965091305673367688201, 207148429137387108862781191631118018341001357820444495793735851294326750651074061923658931845420]
5102 - [249999, 3500]
5103 - [33165873224, 464278585]
5104 - [332911854336799, 4659871351290]
5105 - [9721961, 136068]
5106 - [2355199, 32960]
5107 - [159997202, 2238873]
5108 - [41741976277195612208649, 584046684155382961370]
5109 - [3145, 44]
5110 - [157532110469, 2203731306]
5111 - [1269337898980, 17755148403]
5112 - [143, 2]
5113 [326138956246687557894364376596556926596, 4561049448055548051888279354193031653] [212733237563357562481139726706938389059857982687478070213797709723330664294433, 2975071812756733642853877905331137448306534866699285049551336393266851086376]
5114 [1067083052245, 14921684753] [2277332480777010799080051, 31845353821737837840970]
5115 - [3719, 52]
5116 - [15940430747557443671530166585491256465420742995071999999, 222861364368613227299492024923356922280768485811496000]
5117 - [617686399, 8634960]
5118 - [106493278384978658933, 1488579576694155154]
5119 - [415347262217633599232598201881168952868475859796895599689107591096040789200, 5805221397505373833151811930251467257569851568099381397910630158336152961]
5120 - [5374978561, 75117609]
5121 - [561826924556435303011324050769041011201, 7851003306002713880125573822305193120]
5122 [34907007, 487745] [2436998275396099, 34051436258430]
5123 - [2551582, 35649]
5124 - [790329175, 11040874]
5125 - [1575689951139784122242249, 22010191972314233025492]
5126 - [1502529847005126565, 20986199974649418]
5127 - [764835648724, 10681603755]
5128 - [3410326403, 47623569]
5129 - [16582631468320027306289375, 231545902268859045185784]
5130 - [27870911, 389128]
5131 - [256076101574, 3574934115]
5132 - [6819228556034192223654151, 95190130634805167540130]
5133 - [34103, 476]
5134 - [43821803460545, 611592730344]
5135 - [9244, 129]
5136 - [215, 3]
5137 - [2839529371606495836951232258927703, 39617911950120720942615939154572]
5138 - [458751, 6400]
5139 - [181124355061630786130, 2526606116876327529]
5140 - [154066218432467100261106249, 2148947786232470755088550]
5141 - [11017211429385, 153655419292]
5142 - [59777768839745477, 833630633174378]
5143 - [3599399820583, 50190535404]
5144 - [25363110565, 353632389]
5145 - [12451301493161, 173588943364]
5146 - [5900885732651586303987717649669549, 82258789436314903253370665291730]
5147 - [902631173379035417132292802, 12581523819763677714689493]
5148 - [287, 4]
5149 - [4605983308186086989308261693896604874186856077477681452568257672675658551, 64189044930448169148207289874159047882295753781953697592126773902566020]
5150 - [7088832449, 98780472]
5151 - [1139570980, 15877993]
5152 - [208657, 2907]
5153 [267044921757578036070270244, 3720096900128283835088473] [142625980473021950322730832502698261764918950383639073, 1986865971250732300394127666016328795943901518594824]
5154 - [122946469179389460545, 1712552341576294216]
5155 - [5603349209359682740409, 78042891987194355276]
5156 - [180150127796503885363999220001, 2508869779177583071932580700]
5157 - [224726399, 3129360]
5158 - [2560970713110388546491618966610348517, 35658571658545623784130850811035894]
5159 - [779745, 10856]
5160 - [431, 6]
5161 [1631219180989460622108835320, 22706248681919666395749029] [5321752032855853380512721531189757221714766413759004801, 74077736756528035981034883356885714993421260421808560]
5162 [6107, 85] [74590899, 1038190]
5163 - [810466267082, 11279345011]
5164 - [1006404596467053724238474110565108547487446648475990125456199, 14004883317508508487433316712158694520540007951254065355470]
5165 [27631407778, 384474773] [1526989391588237794569, 21247158466233968788]
5166 - [575, 8]
5167 - [4906404025889969135442117211754180048, 68256509766200193631655372364432903]
5168 - [647, 9]
5169 - [395764212679075858964248421054935, 5504694913756459318822537963564]
5170 - [979648700318749, 13624641858450]
5171 - [1573812626231986237789852031090, 21885967819771821164929308537]
5172 - [863, 12]
5173 - [300122999870033778856393837590759585313158751, 4172804514488935578758979331205592540773400]
5174 - [1942760186817969999, 27008843143323700]
5175 - [1151, 16]
5176 - [1295, 18]
5177 - [11328787639860825777718751, 157450612146847256079000]
5178 - [1727, 24]
5179 - [8024476552777067930775462038789750348745091724190412130, 111504849763452950249246090018358673039757955145589541]
5180 - [2591, 36]
5181 - [3455, 48]
5182 - [5183, 72]
5183 - [72, 1]
5185 [72, 1] [10369, 144]
5186 - [5185, 72]
5187 - [3457, 48]
5188 - [2593, 36]
5189 [4205520498949823283791759282, 58381858883826251737595585] [35372805334174341167659987836596971525553616745266311049, 491052208605454302543738589300944835119030975571939940]
5190 - [1729, 24]
5191 - [110594345541816487236968608120621799, 1534996567020063324809597638753020]
5192 - [1297, 18]
5193 - [1153, 16]
5194 - [132058129474357985250451, 1832374202396986314810]
5195 - [10736772818559, 148963884208]
5196 - [865, 12]
5197 [2287436779974, 31730195029] [10464734044755643374881353, 145161630290165563098492]
5198 - [392261710863, 5440737596]
5199 - [495388394320324, 6870461641505]
5200 - [649, 9]
5201 - [1709533232800506301208536466924415, 23704681305491420878092229667632]
5202 - [577, 8]
5203 - [168867574226, 2341096695]
5204 - [94454226249, 1309340950]
5205 - [66352814172161, 919705915968]
5206 - [58323505380785, 808335284148]
5207 - [158751, 2200]
5208 - [433, 6]
5209 [38442229686776298704507299038139472199524333255318786820, 532637072107989259990720779443014594911795082891071733] [2955610046581729929607660611707817279163611335775025080970135113601811951719514725940456860894130046473211424801, 40951513331334705594468902633951674893319364513532578841999988935024470577074531707398081308337724158309918120]
5210 [4403, 61] [38772819, 537166]
5211 - [228265345, 3162128]
5212 - [2672751616638385611397119427065945883858709922201727, 37021703421393563794622484775418448722550513448488]
5213 [23523482, 325805] [1106708410808649, 15328136106020]
5214 - [446906635, 6189154]
5215 - [12338182352231, 170853558348]
5216 - [211249, 2925]
5217 - [571165151, 7907720]
5218 - [500384990221165763, 6927112430921826]
5219 - [9825, 136]
5220 - [289, 4]
5221 - [49202768066425270007620875286269549469786483895, 680946025776470511660809587339602101437915188]
5222 - [599718351, 8299060]
5223 - [62324256158907288487, 862376852694791596]
5224 - [194390104309027154137909530451, 2689506317000817236277625335]
5225 - [46551, 644]
5226 - [4272683860301, 59103888910]
5227 - [9683010307384024769296301997855230328026, 133931935213815637500312521806479089805]
5228 - [76634623213357447, 1059881317706394]
5229 - [152071153975, 2102991516]
5230 - [9616924921964234429410388494091, 132979709887696141961579032806]
5231 - [49511532302240969215247520, 684563922149752195224473]
5232 - [217, 3]
5233 [2075945582968348417307659390304097735384, 28697270918977139259302965754900025673] [8619100126891591924861508698854919033560420857526103443771442288371354571254913, 119147945614993258159578754187281207492675694814946344181919042556965521026864]
5234 [9667865, 133633] [186935227316451, 2583891607090]
5235 - [201721, 2788]
5236 - [803170174072265, 11099610869022]
5237 [23907274, 330361] [1143115500222153, 15796061891828]
5238 - [28755649, 397320]
5239 - [1520, 21]
5240 - [125100021, 1728191]
5241 - [5045335, 69692]
5242 [8928057691942107, 123312890998265] [159420428301293245552154879198899, 2201889209985356877411634888710]
5243 - [3561105626, 49180725]
5244 - [75132384799, 1037518460]
5245 [75102, 1037] [11280620809, 155761548]
5246 - [1811164299, 25005970]
5247 - [8429543, 116372]
5248 - [5647081537, 77951979]
5249 - [1449, 20]
5250 - [327690749, 4522562]
5251 - [415505666444226883908730439569120303010, 5733976935455543959932119220342209793]
5252 - [758913, 10472]
5253 - [25700004644599, 354592463940]
5254 - [197660437630361103927723538751, 2726934574643540639107434600]
5255 - [8409, 116]
5256 - [145, 2]
5257 - [5202834433488422124710158710909699967, 71758114263000605546372872699578672]
5258 - [12820935599, 176811060]
5259 - [22818217250, 314651731]
5260 - [1575353843571258631, 21721271540791746]
5261 [16610, 229] [551784201, 7607380]
5262 - [432334414555349, 5959974280670]
5263 - [67033, 924]
5264 - [2376415, 32754]
5265 - [147451465208321, 2032122594656]
5266 [164655, 2269] [54222538051, 747204390]
5267 - [110612726, 1524135]
5268 - [37542877077093751, 517254965340750]
5269 - [859041497951, 11834503560]
5270 - [424389, 5846]
5271 - [43924, 605]
5272 - [11393611468262768176276517, 156918339849770447897277]
5273 [944, 13] [1782273, 24544]
5274 - [33867877212256207699, 466356370686002770]
5275 - [154962314660167628644999, 2133609138389526859380]
5276 - [2943025439498755199, 40517405018891640]
5277 - [689527, 9492]
5278 - [24464846251, 336750150]
5279 - [110497689076870567711671358898512285785120, 1520818421263497481477711067615571301841]
5280 - [23761, 327]
5281 [61767112149789660, 849961419457561] [7630352286649386867521564485831201, 104999324637259163134994893238520]
5282 - [19695315601, 270996540]
5283 - [1907162, 26239]
5284 - [5714003133469398668515586785344107222143861249, 78606610452984724779616828341251872585707600]
5285 - [8307279893431, 114271084044]
5286 - [418465136481618658085, 5755667565799353222]
5287 - [2402971170290321650191224, 33047902841336393406195]
5288 - [1782164403, 24507671]
5289 - [22188748434568636220695, 305102680270337373204]
5290 - [4495316905044313921, 61806261844343016]
5291 - [65154374, 895725]
5292 - [3650401, 50180]
5293 - [17415776865457731932913030404087363362399, 239382228019373872451980690151646142920]
5294 - [5364361680452448431387003510773070705295, 73726918600939874004977993139604382036]
5295 - [57330376, 787865]
5296 - [15519021083817312418194098721799, 213250635927676862251922187405]
5297 [2984, 41] [17808513, 244688]
5298 - [160672705601, 2207425880]
5299 - [87471812996966102707195705, 1201631123062198611294924]
5300 - [66249, 910]
5301 - [41423166067036218751, 568937274354582000]
5302 - [3865157, 53082]
5303 - [11103469128, 152474731]
5304 - [2549, 35]
5305 [457188, 6277] [418041734689, 5739538152]
5306 - [3161245692459916335, 43398490874629748]
5307 - [295508462, 4056443]
5308 - [8456241151, 116067840]
5309 [224782, 3085] [101053895049, 1386904940]
5310 - [66839921, 917252]
5311 - [2489970049255953825777440, 34166931146854815833697]
5312 - [361643617, 4961943]
5313 - [12156649, 166780]
5314 - [2654014353867326465, 36407636991964896]
5315 - [18105153126, 248342225]
5316 - [704641456388201495, 9664417975467058]
5317 [7572965892142985328399489882, 103856257997719545354848305] [114699624807122003388143912914615438911560989515640747849, 1572999799004664503820318654592114917447142074984700020]
5318 - [296243537777108101, 4062325500049470]
5319 - [18190255247646076, 249415705986315]
5320 - [1246589, 17091]
5321 [112834284894308468, 1546836642473405] [25463151695219936247242919873014049, 349072412803599500387349112587080]
5322 - [1668788373390527, 22875143661032]
5323 - [27051595898643169137889082, 370778598174271836164349]
5324 - [19845115838503871664511224199, 271978525444035241521360030]
5325 - [194399, 2664]
5326 - [107228825486500840457129073738513668455784679714723215, 1469301655708070109517793433835016740169781978950868]
5327 - [5328, 73]
5328 - [73, 1]
5330 [73, 1] [10659, 146]
5331 - [5330, 73]
5332 - [330126493332151, 4521008342070]
5333 [194618, 2665] [75752331849, 1037313940]
5334 - [1275553201, 17465140]
5335 - [851138997479, 11652880092]
5336 - [3155972095, 43204128]
5337 - [1041175290897652972249601, 14251981551629515852960]
5338 - [747607001651, 10232554710]
5339 - [192758138555036210, 2638048424572971]
5340 - [4072350751, 55728140]
5341 - [158070671986249, 2162917779300]
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5985 - [376421921, 4865672]
5986 - [193420945, 2499972]
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5988 - [22516718751127, 290980715466]
5989 - [3925840666625, 50728907904]
5990 - [3171105521999, 40972954620]
5991 - [49924, 645]
5992 - [321700659967, 4155909192]
5993 [77839703392732, 1005492958445] [12118038848536987262860847649, 156534547297678804782043480]
5994 - [27365201, 353460]
5995 - [139278239, 1798824]
5996 - [18030936640059518302188222125944035879144199, 232856022693229499641496618165313848622390]
5997 - [71788087, 927012]
5998 - [1122466782724635217312200551106960143, 14493399621812846519206257311433924]
5999 - [1833493394514720, 23672270712551]


[参考文献]


Last Update: 2005.06.12
H.Nakao

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