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Integral Points on Conic Curves: x^2-Dy^2=±1(D \in [7000,7999])


[2003.08.16]x2-Dy2=±1 (D \in [7000,7999])の整点


7000≦D≦7999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
7000 - [251, 3]
7001 [628511414391050628788158068555494154032, 7511611713201188529115119645155004205] [790053196039677926886778525044517872807502934188423373909769631031454683714049, 9442267404440923905149084122455778008092376598839700407141038056735755409120]
7002 - [5964562960504723, 71279980798558]
7003 - [44978771360426037700607, 537483980625760951104]
7004 - [34815, 416]
7005 - [203539128357796001, 2431889516391720]
7006 - [45199, 540]
7007 - [164737, 1968]
7008 - [171697, 2051]
7009 - [5968586884642987024718791426530239934766608476057177628626581975, 71292441884619989331785119646323093893923606030453059634026356]
7010 [5024633, 60013] [50493873569379, 603086600458]
7011 - [11785490, 140753]
7012 - [1619748562245139313693000103452757473032993, 19343125492939230340463649844047202598748]
7013 [128714, 1537] [33134587593, 395666836]
7014 - [335, 4]
7015 - [85266658626544, 1018041323277]
7016 - [85240173975114903632499, 1017652578309906544525]
7017 - [222497291978034068692047519383, 2656127946337734210891695308]
7018 - [19603, 234]
7019 - [15685615697050, 187225047411]
7020 - [239104711, 2853774]
7021 - [87261862766258391096934722712700302199, 1041417791973388778184505332303123060]
7022 - [321948451614677799733348011663, 3841987328587009559539470188]
7023 - [4450800512849106735001, 53110060385891688300]
7024 - [387199, 4620]
7025 [1063532, 12689] [2262200630049, 26990315096]
7026 - [7936322853905, 94681527132]
7027 - [185566496006740711828912891832420040080348162, 2213678720923098823821299944198737694117497]
7028 - [503, 6]
7029 - [67606199, 806380]
7030 - [1357895228146512191, 16195285172668296]
7031 - [15531480, 185227]
7032 - [587, 7]
7033 [359613189268989399804, 4288103932146445093] [258643291792427985627560254237832310476833, 3084117461912154475824752367996621923544]
7034 [790481928782662273075, 9425204110454894933] [1249723359463915899597874421789851739911251, 14900907048805323953919464529044159657950]
7035 - [671, 8]
7036 - [58631963360574123344793287378695609914605211181139475028090932524509452339199, 698990900154313179457814330215351010549907053128009551078958074941201007840]
7037 - [14220440018148363126073659999, 169519342525781074087095800]
7038 - [1226177, 14616]
7039 - [128508380551666816104269966903993143430512361302828552255461096345132548454320, 1531707955696692244138961278222210151949452854393085082748314546965620267329]
7040 - [1552321, 18501]
7041 - [2868130584299621998879570685881713415549975, 34180762640228573111371465828664942887492]
7042 - [1007, 12]
7043 - [11325730736312029251122842, 134954505463356627447729]
7044 - [1175, 14]
7045 [3550568894262, 42301663409] [25213078945801762673049289, 300389940551072870918316]
7046 - [1152789225529101564795, 13733416436111660638]
7047 - [87724, 1045]
7048 - [1763, 21]
7049 - [2015, 24]
7050 - [2351, 28]
7051 - [7379479810, 87882093]
7052 - [3527, 42]
7053 - [4703, 56]
7054 - [7055, 84]
7055 - [84, 1]
7057 [84, 1] [14113, 168]
7058 - [7057, 84]
7059 - [4705, 56]
7060 - [3529, 42]
7061 - [15357217722705916255, 182759278829788728]
7062 - [2353, 28]
7063 - [2017, 24]
7064 - [1765, 21]
7065 - [4923521, 58576]
7066 [221550438869442603350392724955, 2635638228419651589230805169] [98169193926485247864419983784591790834103154862780559504051, 1167853612414908040416959766460124959086986125189218584790]
7067 - [11584600899238, 137804541627]
7068 - [1177, 14]
7069 [406177237937712038329540230802610115809782535801140832375342250, 4830995035327972923662560214014468532748670783950897476745773] [329959897237417479079930719367268130844287108946747756845465067136197053482345478567798533562747141388527458080771609270125001, 3924480439880631265362706671358414153430247840443808031794975916836788144503495562545762555845579277397515964288434231618500]
7070 - [1009, 12]
7071 - [1930458774470121023030346828124, 22957263179061715239026652375]
7072 - [1559377, 18543]
7073 - [7972466382330811044537943, 94796186689132823994324]
7074 - [1934944145, 23005724]
7075 - [10575047893934343423895226, 125724269485523670811839]
7076 - [30905719492118049, 367404901945580]
7077 - [673, 8]
7078 - [17106461819726902459394915596118096433933213604901, 203331616465712969444224932491961020788317633210]
7079 - [70320904750093950354331609712040, 835792546000985983471707851891]
7080 - [589, 7]
7081 - [6861852719746708107325107654918145, 81544391275867648710881206856448]
7082 [3477760429, 41325841] [24189635203036528083, 287442749049891578]
7083 - [34625394242, 411420669]
7084 - [505, 6]
7085 [7272329722, 86397989] [105773559170969194569, 1256629326651458116]
7086 - [1936572137674999056828299, 23005575673184773256870]
7087 - [76887537749585427282452, 913323719974329342063]
7088 - [390727, 4641]
7089 - [4770708741351639842945, 56661806270703971696]
7090 [2344428417, 27842861] [10992689204874251779, 130551189077962074]
7091 - [84182807808126, 999699935975]
7092 - [308897, 3668]
7093 [2407454428283982, 28585322415305] [11591673648528309261650475552649, 137635722065302788501366289020]
7094 - [4936772882649045112237925, 58613486574420546366114]
7095 - [79936, 949]
7096 - [125288009537733004908595972131215, 1487314137864278965417277122362]
7097 - [133882677702552613599, 1589230850943725320]
7098 - [337, 4]
7099 - [192974709385326093771543352497161817833510, 2290349753853833488181536949443416862251]
7100 - [24220799, 287448]
7101 - [16116667272575, 191256182832]
7102 - [63101740539450381138159947, 748774428961892787385698]
7103 - [482655173746128768, 5726853303536671]
7104 - [174049, 2065]
7105 - [55805391361, 662055072]
7106 - [6132769345, 72751848]
7107 - [2782, 33]
7108 - [114654350050825314539681710339770969616513, 1359930854194570873309609490668823879736]
7109 [52776148611782, 625941054065] [5570643724585798251498431049, 66069516183099823115987660]
7110 - [6616066879, 78463032]
7111 - [325901217679499184254702205260908825, 3864743218760161362135436341626628]
7112 - [253, 3]
7113 - [352251337537997735951111524667287, 4176632335827305364627833723444]
7114 [332746065747478633199600011728120848835, 3945081674987952424272619358871907697] [221439888540850746592429668085828602910183625447673731027501289756401841714451, 2625420812809428699729415794135547219173590582090719179885703174750819965990]
7115 - [238552101469884006, 2828106725006147]
7116 - [14322630756680320536199, 169787152981675781310]
7117 - [98619492599, 1168999380]
7118 - [738154081304213933583, 8749193739164016004]
7119 - [101249, 1200]
7120 - [43468489, 515151]
7121 [1951842224669398868885453230644415890765832, 23129924548813681949778523811101083066265] [7619376140004776260850059431126175072262604854878176704110980152692481440654917304449, 90291926775583677737732252158597857665647746359147332490244662114728507195307714960]
7122 - [1308196087697, 15501433492]
7123 - [105140672929207947055493402, 1245774050081336037185319]
7124 - [44128916375049, 522830973010]
7125 - [1358453212067130751, 16093564713123984]
7126 - [68200121051, 807908610]
7127 - [4673451370149133916711928, 55358504417895102341477]
7128 - [30580901, 362215]
7129 [20263332824783762428229892729259264345268005126010103061068, 239991892475381067492566707958688434280468674153412958325] [821205314335918185705903485323002421157009001380419984918559496635491852453486965527464542522458264281957887474601249, 9726071184956728850464556672466761202238629568408178764096779185235455735122701272615805370011114596537160027982200]
7130 - [26275661, 311178]
7131 - [2555627468690, 30263721323]
7132 - [180690202239136431432943425566473249894629172351, 2139582005647906855267732858365012397951835640]
7133 - [585509247, 6932624]
7134 - [50996365377535, 603771586944]
7135 - [19246925736067952865859804, 227858052879524844906423]
7136 - [110166015, 1304128]
7137 - [4393, 52]
7138 - [374229190611501061638401, 4429445765314124656560]
7139 - [669109811262650, 7919152514079]
7140 - [169, 2]
7141 [3970119829031264403253838277912655404918, 46981199266976992924202370966699507265] [31523702913734472191201616795822621039434720448273263097398369561396077077173449, 373041981602988927308800453996837544359642608737128301705370736603939315458540]
7142 - [3772164096577976530300730205634117, 44635525712489905661529193985442]
7143 - [103936481068, 1229780731]
7144 - [78064935471648262925, 923602887749861589]
7145 - [2541473641, 30066612]
7146 - [6685438210471646801, 79085774719282540]
7147 - [3221704897533680102, 38108676508641843]
7148 - [93507366151, 1105995990]
7149 - [74211941812670223571779557237280298338043304746868299255, 877710202967165839392637004879928394619256752154408876]
7150 - [631317134449, 7466112948]
7151 - [14899502942470983534802910074321191065698587840, 176192894928494963216227289946438837766256807]
7152 - [43807, 518]
7153 - [1755107117082882144034277423928821979198857245151, 20751978786983686347099961526130753555971474760]
7154 - [3536236801, 41808720]
7155 - [1163628309626, 13756547735]
7156 - [13673687937600285436522338047798889300505982960692087644059539022368201, 161640616512356282610885358004578106409674117633489119824838738784130]
7157 - [37842849, 447320]
7158 - [313779631558277, 3708761463446]
7159 - [389825726540685126406277027294113105746231645954870338429875941495413080520, 4607276914722018315479111193398277059932369598795329812471043303711283019]
7160 - [60501, 715]
7161 - [265047582185, 3132110028]
7162 [382716516708311101235551894024461, 4522307057551374209866063501909] [292943864322685940639384097140012218498878556923265811517732681043, 3461523209102947441343429747010043361977096601110942689932392098]
7163 - [45618, 539]
7164 - [529178298454520220799, 6252075831211685160]
7165 [9417175494581270042653960421787222, 111253214069156912601413141655677] [177366388591483976076984592949375996739160385454541538605401284954569, 2095382082450937318156193311319311463709631011384845648320964718588]
7166 - [980370050116423351527963895555409575935, 11581148578417339179401711895660347392]
7167 - [2182819151527, 25783926428]
7168 - [32257, 381]
7169 - [3336390496309794941468515769974835415, 39404660060240966962772291562631564]
7170 - [958465925999, 11319235620]
7171 - [8407758739865457596875001, 99286540800775575202500]
7172 - [262535353551703, 3100042545642]
7173 - [2985392710258282817491643850401, 35249345099060068274951045640]
7174 - [60212800403131083325897445, 710899387200043304248326]
7175 - [95550624, 1128035]
7176 - [12582335, 148532]
7177 [24431236809771434577360292137605304633207861311402797368, 288385871781079245137602514193710625459781499177596405] [1193770664110261408331750731923318151783284096816783924044017037371104725707319470217598605174243809231335454849, 14091247052151856953331690162111416066192674254865361907767951573299686044021923442064157506592033903000524080]
7178 [5507, 65] [60654099, 715910]
7179 - [2414551595737586572062311598890, 28497352434261176303034117309]
7180 - [2389684563359, 28201899204]
7181 - [283928055, 3350548]
7182 - [5771249, 68100]
7183 - [639416086660913161224686183, 7544502816321054331100844]
7184 - [71798771299708449, 847098378350530]
7185 - [7458830386698719, 87994868213704]
7186 [11151485721778906239225, 131549477126420901929] [248711267606077626902074980283907265857201251, 2933944231765527016395481040829899875930050]
7187 - [17681122384179322376026, 208562396177384795655]
7188 - [15908371013339999, 187638380876700]
7189 - [198443854115140053927012477458800951, 2340471792609433618559766224905140]
7190 - [463948014228479, 5471480742624]
7191 - [424, 5]
7192 - [2089768622363, 24641853123]
7193 [271286955514355824995547305368, 3198702734584968645739128685] [147193224464496152727343497540659670076377927378971683230849, 1735532652922001433272013358378872467835138394063886562160]
7194 - [496151215, 5849636]
7195 - [901922831783152265525759, 10632955147190261980512]
7196 - [18290603548799, 215616731880]
7197 - [3612834765251442938716596893030399, 42586539150299346578430099541440]
7198 - [47072896764806468984194727209099, 554836474515118341300200093790]
7199 - [3110817959787699994560, 36663887431752765551]
7200 - [19601, 231]
7201 - [3095734769962218915816420786293111278319706923684229579799, 36481050824906466203274445163780489099903514974260150020]
7202 [60169, 709] [7240617123, 85319642]
7203 - [5170128475599457, 60917858512904]
7204 - [806667238174283887339603999510156079461856181188670036342049, 9504024930874901591191134153359210075667134803225375111140]
7205 - [1502340489, 17699108]
7206 - [5182784353201, 61054265380]
7207 - [26662177269858641140812012554467367781169230562131224, 314064139500049557078200318875410564445350600716595]
7208 - [849, 10]
7209 - [500006000027000056000052500018000001, 5888947777989778107555761666702000]
7210 - [230361369871681, 2712951438984]
7211 - [271861382011039991627375849740014096370, 3201472476818166141956657274189788253]
7212 - [203137, 2392]
7213 [27010686, 318037] [1459154316381193, 17180795086764]
7214 - [116591392021407561959391063485329260567216015, 1372708802226337864110634361392985678579596]
7215 - [1444, 17]
7216 - [4319198765640199, 50845781646465]
7217 - [17031059361563594986527455967, 200476425403227212088195608]
7218 - [295496099, 3478110]
7219 - [21526977145353537263441936256972789903833833134426887129460879846209375980786628090, 253363779455142500367526085859154781980824256994032427070466692202247158979105289]
7220 - [2889, 34]
7221 - [306935, 3612]
7222 - [11265943165147, 132568033458]
7223 - [7224, 85]
7224 - [85, 1]
7226 [85, 1] [14451, 170]
7227 - [7226, 85]
7228 - [146471428766233, 1722835634586]
7229 [307190, 3613] [188731392201, 2219754940]
7230 - [2891, 34]
7231 - [90931817759840960624, 1069342165929210975]
7232 - [1204353, 14162]
7233 - [23213719252787982113946404272343, 272951506231817830610094230516]
7234 - [932325155, 10961706]
7235 - [1446, 17]
7236 - [546665912276384215, 6426473409391478]
7237 [49571973020440031963192923874571772808382, 582715966986885611182876763740835771105] [4914761018278468851229736277718005980265752506550368987509081508736282078578915849, 57772760388107035724641759022033656712082610933830473100536526075261100754804220]
7238 - [174747, 2054]
7239 - [10497497445145, 123380489604]
7240 - [104491504202900419, 1228037695501437]
7241 [89728054767267340, 1054457254294781] [16102247624635454441223782061351201, 189228796526208908265268387505080]
7242 - [851, 10]
7243 - [104115493199608462993440824422035973229358396242, 1223365188147034227787963846474081808002905171]
7244 - [43035912199, 505640430]
7245 - [1514868641, 17797368]
7246 - [2199750028450802072713649401334513168136506716899142726183703725409128435460495, 25841883670735961292405078752389242212407204804745130303566287543720920204588]
7247 - [3480542614396512285802128, 40885359876352613483017]
7248 - [1653751, 19425]
7249 - [14518651659981320194199, 170524677024744665220]
7250 [22816057, 267961] [1041144914054499, 12227626899554]
7251 - [73703059016198675409890, 865538839612394667543]
7252 - [1555849, 18270]
7253 [16168561002266197009496602318, 189850843397466252517712825] [522844729768006578354524873257000278913349495172485946249, 6139229885607239525663578360068682519726019899906656700]
7254 - [76048854592049, 892902217860]
7255 - [257117934081432095900426540249, 3018656257304925965130233580]
7256 - [789064983271716805, 9263265970911627]
7257 - [56012037389399, 657510675460]
7258 - [227593403628642041505745517, 2671475457658067593753506]
7259 - [426, 5]
7260 - [457470751, 5369020]
7261 [217711143588806202588285321465228675999810, 2554950207128704292030316377040025099229] [94796284085491584177326111398143271222501937541961601715168329101112378206240072201, 1112482262812894977577062744793669341568462039689351599483902066636877372070292980]
7262 - [3841599, 45080]
7263 - [557319100702424477127724, 6539520500600342495415]
7264 - [572304824258877032120691890438449, 6714899066664621820084698482355]
7265 [707026854272, 8295032657] [999773945323519849299969, 11729621691124439921408]
7266 - [4820497949, 56551510]
7267 - [57032515249947238998151, 669029002929955940580]
7268 - [23937367869663, 280781787676]
7269 - [4935359037442431306591514089061870934015, 57887049981611822215555690912875075264]
7270 - [5329044493758335053247634368891, 62500305601955505531690118638]
7271 - [71014926895001, 832822734300]
7272 - [19731763, 231387]
7273 - [11745860690143, 137729842824]
7274 [1421741995235468392693157, 16669944095838781285765] [4042700602032261259658940552027857585735109253299, 47400719158563090092248272722826198319154020210]
7275 - [168199, 1972]
7276 - [3885590216227263850754059917369799, 45552335843239624551805275372270]
7277 - [1917761311473288338261404065151, 22481141831525402071060255920]
7278 - [27819766068533, 326097484086]
7279 - [501138820, 5873841]
7280 - [8191, 96]
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7999 - [2806758922220, 31382480199]


[参考文献]


Last Update: 2005.06.12
H.Nakao

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