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Integral Points on Conic Curves: x^2-Dy^2=±1(D \in [4000,4999])


[2003.08.16]x2-Dy2=±1 (D \in [4000,4999])の整点


4000≦D≦4999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
4000 - [3117419602578001, 49290731833017]
4001 [1409717240, 22286801] [3974605393506435201, 62836175188298480]
4002 - [5567, 88]
4003 - [10675090753927503722008879537371122, 168724745136660516665415874096719]
4004 - [1060905, 16766]
4005 - [43468489, 686868]
4006 - [3627681448972124688885752841837120064353235414365037445, 57315709347413016502127480790113183410147231351775502]
4007 - [7829026470560460024, 123679605193772915]
4008 - [206869247, 3267624]
4009 - [3799, 60]
4010 - [7219, 114]
4011 - [190, 3]
4012 - [162937351, 2572410]
4013 [583202494, 9206293] [680250298015640073, 10738266076189484]
4014 - [24273101721960449, 383121559493120]
4015 - [742212453896, 11713467111]
4016 - [27009633024199, 426208229865]
4017 - [13183, 208]
4018 - [5647081537, 89087976]
4019 - [1708604365567350951677221730, 26951473159328913297971289]
4020 - [2950149761, 46529784]
4021 [261789723082170, 4128436006841] [137067718222878504169143817801, 2161564237986730163450249940]
4022 - [899697265462117, 14186503428702]
4023 - [12966724, 204435]
4024 - [14125267563780214605455, 222673070127787460874]
4025 - [277301249, 4370880]
4026 - [84149464255, 1326216632]
4027 - [489926383300155323805655713528988632537844064331002, 7720403744882820167494955973824537167233515551083]
4028 - [453151, 7140]
4029 - [40692425, 641084]
4030 - [9579769109, 150904614]
4031 - [78541711170201, 1237069102220]
4032 - [127, 2]
4033 [24323997707922974376, 383019462789474113] [1183313728990084222121478786725505178753, 18633129069962114596023657959628656976]
4034 - [18656897487784515, 293745673232494]
4035 - [711506, 11201]
4036 - [583201, 9180]
4037 - [2235709805703145399, 35187309169758540]
4038 - [325733, 5126]
4039 - [22288270864881375590235560, 350702975339090911793571]
4040 - [3395619, 53423]
4041 - [10310127120295675365715024803971201, 162188327294782939531953399007920]
4042 - [61255554861860333, 963490248543642]
4043 - [221686399, 3486480]
4044 - [141994951, 2232890]
4045 [318, 5] [202249, 3180]
4046 - [9743412645135, 153178621412]
4047 - [1781249, 28000]
4048 - [3222617399, 50651055]
4049 [38478152590707323336680, 604700495089193315993] [2961136453587513397317964548610024257266844801, 46535515843436489689330555084695444735046480]
4050 - [19601, 308]
4051 - [5383417627373949351123839808517440621285033901490, 84581805341317262274629872520787545399261115657]
4052 - [309159979019115849, 4856781334654730]
4053 - [3483649, 54720]
4054 - [13971438861629094598893146979059394329145661881201019971365, 219431646813187437183447298305437210029482532725398231934]
4055 - [1298859976089, 20397028612]
4056 - [4656965, 73123]
4057 [13833399844287905529750976821544275850044, 217183299242916279634890326216262815029] [382725902503889297913541379676115186731788253687652856246148935722378237549603873, 6008766835857783307255897900772197522343201654498602681868116689271634627022552]
4058 [536693, 8425] [576078752499, 9043277050]
4059 - [46471490, 729419]
4060 - [352871, 5538]
4061 - [18577348099802281296876218751, 291519240741564348477958000]
4062 - [1951781642507, 30623954398]
4063 - [7649, 120]
4064 - [255, 4]
4065 - [8671, 136]
4066 - [343977292342747234626065, 5394436514982636408492]
4067 - [361643617, 5670792]
4068 - [2900932297217, 45482792496]
4069 - [363483145, 5698236]
4070 - [18501, 290]
4071 - [96879480545, 1518382712]
4072 - [15155578752298003, 237502749088167]
4073 [2184422186219192768, 34227830589326245] [9543400575293275373815894331087003649, 149536065050952394599162121793192320]
4074 - [154226701, 2416290]
4075 - [64080026, 1003827]
4076 - [74174332129101914180385799, 1161813870115399424692470]
4077 - [1653751, 25900]
4078 - [70221293770832713806532587704441992463, 1099626547115668509621755638589441916]
4079 - [189716843606453532684519911280, 2970496451095500078889982759]
4080 - [511, 8]
4081 - [604530652265, 9463134852]
4082 [1460857, 22865] [4268206348899, 66804990610]
4083 - [40819384890026, 638817442935]
4084 - [198723867690977573219668252231077415636351801801, 3109618879607381413593704751509716307988342270]
4085 - [8801188553079, 137703600188]
4086 - [16916040084175685, 264636366164922]
4087 - [4601182724, 71972595]
4088 - [1023, 16]
4089 - [1285759776147201449, 20107185282015420]
4090 - [1251270322579, 19565434194]
4091 - [37831919632484839132490, 591484868211020767467]
4092 - [2047, 32]
4093 [18008443854, 281485037] [648608100085340746633, 10138214969111225196]
4094 - [4095, 64]
4095 - [64, 1]
4097 [64, 1] [8193, 128]
4098 - [4097, 64]
4099 - [6290679704195680536253612607008970662569749959960678667690, 98255894580947570793022586715791022877883393268276434001]
4100 - [2049, 32]
4101 - [15038410460012428677053740572796415, 234831877148720411637761404955232]
4102 - [10141222990572827, 158340679489542]
4103 - [36076932, 563221]
4104 - [1025, 16]
4105 - [3830995270998176489, 59793645893686188]
4106 [273293, 4265] [149378127699, 2331189290]
4107 - [9863382151, 153908820]
4108 - [133150393, 2077434]
4109 - [46013140309107764048945975, 717817105677092067911844]
4110 - [244530751, 3814280]
4111 - [22600970918684145317406830884887526438186669303416178086560, 352495322229152178879614940884523956622557436044222529897]
4112 - [513, 8]
4113 - [6983244756398928218113, 108887470523463284544]
4114 - [839492675, 13088346]
4115 - [82702446, 1289239]
4116 - [97379496466615, 1517853447942]
4117 - [1837945102852582416613765930145532519988909151, 28644556460037454057952889000429618179182680]
4118 - [1893364361423, 29504688036]
4119 - [338590853596324, 5275690702755]
4120 - [884307011291, 13776993717]
4121 [49245443320, 767122541] [4850227375566665244801, 75554579224619752240]
4122 - [1048728401, 16334620]
4123 - [34490562553, 537147564]
4124 - [849523403982641460728723279999, 13228665032561244608342903400]
4125 - [23400586355066999, 364346635403604]
4126 - [21463508140861728553057577651533912660709375, 334145868438155779219711421198468455829568]
4127 - [2826522857010387648, 43998236250093167]
4128 - [257, 4]
4129 [1543490618196745649235160051135883919346588932, 24020472863889191534318386913393290031716825] [4764726576922744102984571359612477560223126002281056165101651310774602699688985807569801249, 74150749020124963306733757010403185701758477080059295307067580181294296734592311006361800]
4130 - [4064509, 63246]
4131 - [499850, 7777]
4132 - [69833593956354694952807071952492833, 1086386191744902921165535640904228]
4133 [176986, 2753] [62648088393, 974484916]
4134 - [69973806395, 1088304094]
4135 - [1874230971572396404, 29146429030397403]
4136 - [15885, 247]
4137 - [4496973089503, 69916153672]
4138 [603757498350340221, 9385713524810297] [729046233628522149364384772900657683, 11333389835944837583763268868111274]
4139 - [37250, 579]
4140 - [2535751, 39410]
4141 [284839647896119154334566816718, 4426371133735626085552123445] [162267250027170273968445205418073637423098775985631608583049, 2521611990381602965333531298891794957337725204918051507020]
4142 - [6524523, 101378]
4143 - [2114208499417, 32846594404]
4144 - [847225, 13161]
4145 - [249494661161, 3875243436]
4146 - [12778583277142710981185, 198457747912327754312]
4147 - [94627378, 1469433]
4148 - [8710152963849, 135240388010]
4149 - [2795911984444305802027420016801, 43406201108963787457810483080]
4150 - [5786139071247158449, 89818297639168692]
4151 - [203400, 3157]
4152 - [15404267, 239063]
4153 [978927886204995237379992467521844556, 15190418349378359832517839447959173] [1916599612779560209557902914405290722142964324484199267444482089253674273, 29740648250653061240852425711771486063436763063214863104698661480624376]
4154 - [41181951, 638960]
4155 - [379214, 5883]
4156 - [486481895944288701289625276844927549121653360703500799, 7546210464069638231661211640210258675267960456275920]
4157 [7180655467682, 111371502125] [103123625891102804292906249, 1599440771355677463648500]
4158 - [317899, 4930]
4159 - [5414767271524082813120, 83962494925794507231]
4160 - [129, 2]
4161 - [11095, 172]
4162 - [75602028173705811683, 1171878019769582982]
4163 - [24208609726, 375203295]
4164 - [770918649927575, 11946843971746]
4165 - [285769, 4428]
4166 - [59418908613165155383083738565, 920587423974469760615286642]
4167 - [247512720456368, 3834297208387]
4168 - [1302499, 20175]
4169 - [17604635555034997944764892094999, 272653508985316114448065655700]
4170 - [26856191, 415888]
4171 - [775, 12]
4172 - [576927, 8932]
4173 - [16848649, 260820]
4174 - [1424156508991205142208681039557490896776199898778313581829510488975, 22043547972406602245188180037336225229518423057650028204781695724]
4175 - [18966024, 293527]
4176 - [192119201, 2972970]
4177 [4705982784845200596839958307656, 72814537696742108814167666009] [44292547942518779144450202494224889059611070169104663096428673, 685327921774660535374479530024713742949913230202310151329808]
4178 - [263218177, 4072224]
4179 - [2677345, 41416]
4180 - [456191, 7056]
4181 [489181478614821790, 7565365622404889] [478597038039566696511234146917608201, 7401673482859530298834759919462620]
4182 - [37637, 582]
4183 - [317558171528, 4909975899]
4184 - [3987042510565, 61638921081]
4185 - [15990898437631, 247186719456]
4186 - [18855674947565, 291435512322]
4187 - [143493953718, 2217594427]
4188 - [136807, 2114]
4189 - [2348310155551200245641645845518123357620381521252013751, 36282756659471626090344570914713715637788216718375900]
4190 - [25491871648821, 393817228654]
4191 - [29371924, 453705]
4192 - [22041817899174577, 340437014378103]
4193 - [19167, 296]
4194 - [938319425, 14488936]
4195 - [45772086899846122191836963999, 706699414022674604276153640]
4196 - [4720747718766511296768801, 72877430538193335610660]
4197 - [2229399257939085408333751, 34412669824993224540300]
4198 - [113978639776334919899595657028901, 1759147488675595201885659246810]
4199 - [324, 5]
4200 - [8749, 135]
4201 [2769671929650196669406297005338979393158336660780, 42731878878430983047722050842457079024438077101] [15342165195784487937181167063910620379274871789035457823176568529478448214293546222453921580416801, 236706570861604845270759494315006025078312806937322254908546450590640947579972569674113045597560]
4202 - [8607991437, 132792578]
4203 - [1625626, 25075]
4204 - [1825512460897583376717662517209872247435085310431124999, 28154864923511321010688354478768406951703858826937750]
4205 - [299537289, 4619212]
4206 - [1826014690238699, 28155914188610]
4207 - [383447171307218768, 5911793862730983]
4208 - [38713200767, 596789556]
4209 - [1222672005355632215, 18846057234622156]
4210 [155019807, 2389165] [48062281124634499, 740735794382310]
4211 - [174844298319090500142303314489781850, 2694380047628390959995251257521897]
4212 - [649, 10]
4213 - [19071901038149286317976796874999, 293831434246702011246505462500]
4214 - [4505948689285, 69412706154]
4215 - [844, 13]
4216 - [3355576256056895, 51679322502708]
4217 [24841507818878476, 382539382432741] [1234201021430800915937244912165153, 19005710119463758154382245165432]
4218 - [231421901, 3563290]
4219 - [97368731966766164199033274737192581210, 1499045280812594827427418555254641461]
4220 - [1689, 26]
4221 - [137215, 2112]
4222 - [559884677381394885476016891268814708946565953599, 8616670137323363145176951081959937441003890680]
4223 - [4224, 65]
4224 - [65, 1]
4226 [65, 1] [8451, 130]
4227 - [4226, 65]
4228 - [239637339568529407, 3685420100066496]
4229 [137410, 2113] [37763016201, 580694660]
4230 - [1691, 26]
4231 - [1448005395154038127926578071623745469720, 22261204914463309108155324946001318973]
4232 - [131836323, 2026573]
4233 - [39016567127, 599687396]
4234 [14224977682275, 218613092017] [404699980122443661698351251, 6219532709989911929797350]
4235 - [846, 13]
4236 - [71604224024098584199, 1100172200669895410]
4237 - [67008760418986958696434461874237094445151, 1029443111985341797799944606703773530120]
4238 - [651, 10]
4239 - [7838695, 120396]
4240 - [73738369, 1132428]
4241 [30618389973781211518873532, 470162745703974776753345] [1874971609173091637204298392650019925688492420310049, 28791252598216053366957368719542322507429225929080]
4242 - [320573, 4922]
4243 - [71495387886939108299769509927142362, 1097593460464898075426812651808199]
4244 - [170800615664635332564330517881801, 2621813191078083737460891337130]
4245 - [303821441, 4663152]
4246 - [1036159035641953894068021395045, 15901438855896510581442030162]
4247 - [21409128, 328517]
4248 - [306917, 4709]
4249 - [1406721390390084009875311660957976221637955862015, 21580660160397807236549009676230375609895828576]
4250 [5984693, 91801] [71633100608499, 1098801604186]
4251 - [326, 5]
4252 - [6092317532089106967495481012351, 93429904039920864102405886440]
4253 [89755568161882, 1376301898765] [16112124032124491488315563849, 247061517771859154991751460]
4254 - [1879917009784506005, 28823049970624234]
4255 - [24444979624, 374748495]
4256 - [938449, 14385]
4257 - [15137, 232]
4258 - [133197261443, 2041232466]
4259 - [200236646655773016130, 3068242939661179281]
4260 - [82667999, 1266580]
4261 [493849011425474442917611131330913534583995157296610418, 7565513692976193152924229576191347262650745668520785] [487773692171836773724609849913554117111338210033172214202613754243355294551180678058174336686937984132269449, 7472442916404366718042414428150210943686325241177441866467283025312332082757122658434098509179768961076260]
4262 - [911908936708901, 13968338442630]
4263 - [1567, 24]
4264 - [23597172197299, 361369390935]
4265 [5632821579008, 86251464389] [63457357881876356772528129, 971678219662798523892224]
4266 - [29002323118011949, 444040273216890]
4267 - [424981762433, 6505923792]
4268 - [19207, 294]
4269 - [69744788185238404612918031666935, 1067452803720808529835559078764]
4270 - [5489, 84]
4271 - [1234320, 18887]
4272 - [11539207, 176547]
4273 [102814765256925009974440561376708232, 1572856284250054995873985227611945] [21141751909673188224599970798390097292353994900204917977410792113131649, 323425699296097444314333318890638436656435063061715291977916766062480]
4274 [1455593, 22265] [4237501963299, 64817556290]
4275 - [57799, 884]
4276 - [742925865816843150858935268959512942700219559049, 11361263456141505036160120355392731361759572870]
4277 - [17482401, 267320]
4278 - [380927, 5824]
4279 - [4492490201, 68677740]
4280 - [2948491, 45069]
4281 - [3242990727575, 49564769748]
4282 [14667598989315275691, 224148427478728801] [430276920222724993868470303118671054963, 6575438496687221861825403599073752982]
4283 - [346922, 5301]
4284 - [28799, 440]
4285 [40614099220800256909842, 620442318886947655757] [3299010111034016070952535152336459733832929929, 50397411800115770613417751386967405602520788]
4286 - [580010189055, 8859506672]
4287 - [1856659687, 28356692]
4288 - [45526445508292066657, 695242568908206189]
4289 [2230562470014106565360, 34059350954149342753] [9950817865270864101090870147172511903859201, 151943019982729350360724331953492473672160]
4290 - [131, 2]
4291 - [4532168345760066973943482724665, 69187362629241754841897352108]
4292 - [4116510849, 62834680]
4293 - [8777860001, 133970200]
4294 - [378769445, 5780214]
4295 - [910482345639, 13892805164]
4296 - [3489425, 53238]
4297 [63986853750790070065951916604, 976130941913530064919424381] [8188634905849994516050520990507605191704599727481941785633, 124919095643684010495765085150574542783018505510792644248]
4298 - [10620973, 162006]
4299 - [5771445002054552513999330, 88023947094490260086451]
4300 - [57032515249947238998151, 869737703808942722754]
4301 - [952159246345, 14518604268]
4302 - [1617319577991743, 24658158552632]
4303 - [68052293272123172, 1037425913523681]
4304 - [13449, 205]
4305 - [5249, 80]
4306 [4039378465204593, 61557012315805] [32633156770317226683242696591299, 497304139861593259920104984730]
4307 - [80838082, 1231767]
4308 - [23522399, 358380]
4309 - [31606044107117492065564284412616218425260286399382514551, 481484038757125747386247094446645420403225797916861820]
4310 - [447591232079, 6817779252]
4311 - [17873503027199, 272220399360]
4312 - [197, 3]
4313 - [788045621202748469015767, 11999458032208557223524]
4314 - [4875549054850291162799, 74230683596273336860]
4315 - [43445954316823546006, 661392005585214267]
4316 - [65216016291838751, 992689774856700]
4317 - [12535327583, 190785192]
4318 - [1373633, 20904]
4319 - [34210800, 520561]
4320 - [55989361, 851851]
4321 - [67049, 1020]
4322 - [4153443, 63178]
4323 - [263, 4]
4324 - [293215056101715119615, 4459061109364003824]
4325 [1118, 17] [2499849, 38012]
4326 - [120595938049, 1833535920]
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4998 - [4120901, 58290]
4999 - [36602597872432826422774598212839995768873090103501521163739417443181640, 517690674949038127261225892293391610962526870191086544534450818687299]


[参考文献]


Last Update: 2005.06.12
H.Nakao

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