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Integral Points on Conic Curves: x^2-Dy^2=±1(D \in [3000,3999])


[2003.08.16]x2-Dy2=±1 (D \in [3000,3999])の整点


3000≦D≦3999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
3000 - [2550251, 46561]
3001 [4758959166078874909404390921598306320, 86871832084583873601621533570831549] [45295384688812281004322225610616890677451950697118754577855623785103884801, 826839003145990640915374486441398199564121085363552711238974624844179360]
3002 - [292143, 5332]
3003 - [274, 5]
3004 - [106384988516182508970518277291361767313787214963199, 1941021682936914823936591197542079139112649995280]
3005 - [109627209, 1999844]
3006 - [63804373719695, 1163739999748]
3007 - [40038809408, 730153953]
3008 - [4607, 84]
3009 - [1234783508951, 22510219340]
3010 - [31579631, 575604]
3011 - [149586342603777656598640130, 2726067254254307194188447]
3012 - [308526027863, 5621656742]
3013 - [7710900593307374464807508351, 140477101752503703088259280]
3014 - [549, 10]
3015 - [604, 11]
3016 - [836977699, 15240465]
3017 - [1315978715892977151, 23958587494071520]
3018 - [1831739126447, 33342948716]
3019 - [11752562541659941018442526415237539460392094825860314330, 213895188053752098546071055592725565706690871236169789]
3020 - [1209, 22]
3021 - [83105, 1512]
3022 - [39309920653121065158848783, 715080503387676916644252]
3023 - [3024, 55]
3024 - [55, 1]
3026 [55, 1] [6051, 110]
3027 - [3026, 55]
3028 - [3750107388553, 68149985694]
3029 [83270, 1513] [13867785801, 251975020]
3030 - [1211, 22]
3031 - [3311363339961862760, 60146985826992027]
3032 - [413959717, 7517847]
3033 - [2063810353129713793, 37474304521921584]
3034 - [4055973299, 73635510]
3035 - [606, 11]
3036 - [551, 10]
3037 [1006348625514413652019842018, 18261063295668900784053085] [2025475112149499136094828760894883227770506355356624649, 36753991896056214037967550797040674936227630851051060]
3038 - [7937, 144]
3039 - [567355653318700203124, 10291769160627327625]
3040 - [5412368881, 98163627]
3041 [101333935702437060876068, 1837581883045655029625] [20537133049891296860461720054737722655310281249, 372418808769023251700286548550077625987029000]
3042 - [26102926097, 473270668]
3043 - [429778, 7791]
3044 - [1280001, 23200]
3045 - [111823361, 2026464]
3046 - [858084803913933646792276518543893385687827805632645, 15547668115105561077642022265612613794549714209362]
3047 - [276, 5]
3048 - [6349, 115]
3049 [35430670275765809983489042732648396596180, 641653630983894845799886516985041024493] [2510664792380069795324386798405024245032324912355903876879862308146915619981184801, 45468436461276573746714417291922208349562231907536616332825023982269842420473480]
3050 [5357, 97] [57394899, 1039258]
3051 - [3761311617998090, 68095468410093]
3052 - [719724601, 13027890]
3053 - [21090261599, 381696840]
3054 - [367499, 6650]
3055 - [1015624, 18375]
3056 - [161784071999999, 2926571151000]
3057 - [2956717664784599, 53476396736620]
3058 - [201526983840401, 3644302882260]
3059 - [6863751, 124100]
3060 - [285769, 5166]
3061 [7501003966915325475620068851198947387333727886305918, 135577534004649595608478940148232618754255880773065] [112530121023358898404903532500783683343457018270681330586871060096531509537062002479141495461904563645449, 2033935240786948099791397324693815401325711604511166489710877622423387335625737233177364957449848997340]
3062 - [27557, 498]
3063 - [2447710449127, 44226904484]
3064 - [145933611945744638015, 2636397864432812604]
3065 [95604128, 1726877] [18280298581280769, 330193139496512]
3066 - [1251949, 22610]
3067 - [20138859064798731994238851418239777207226, 363645296509166562391011303110863282485]
3068 - [1948377887, 35175924]
3069 - [10626551, 191820]
3070 - [11832257143970394381611, 213549427580319742026]
3071 - [665, 12]
3072 - [708158977, 12776743]
3073 - [2776937178639512026642007078623, 50093891973498258238271190744]
3074 [1122457, 20245] [2519819433699, 45448283930]
3075 - [7263026, 130977]
3076 - [535781868388881310859702308423201, 9660394162520168608912227752580]
3077 [419282318, 7558625] [351595324374906249, 6338395621785500]
3078 - [202501, 3650]
3079 - [56707696356679785946525966318147373960, 1021967678730302928114382808347749891]
3080 - [111, 2]
3081 - [8215, 148]
3082 - [48832848419533613, 879621306039882]
3083 - [30280839133349026, 545357316089235]
3084 - [17869879172579649799, 321783989163189410]
3085 [147384419857347549222, 2653529939520359861] [43444334433373805162723128385939425610569, 782177941420621534438776335999701156284]
3086 - [536433588593295, 9656461256372]
3087 - [130576328, 2350153]
3088 - [6224323426849, 112009151010]
3089 [6689389081410197026019960, 120358704037480100216953] [89495852564979919150002896448538279482556636803201, 1610252401282001559195724037331914356364216763760]
3090 - [119069, 2142]
3091 - [46913101361185187371233770, 843809949632200546432167]
3092 - [3607394696649, 64874484490]
3093 - [2644971939878399, 47558824204320]
3094 - [5499853978555, 98876026314]
3095 - [10700785269159, 192346958132]
3096 - [10405, 187]
3097 - [136853545181672549008645399, 2459152432067478310676940]
3098 [49896339893, 896453945] [4979289469435566502899, 89459541476281455770]
3099 - [27890, 501]
3100 - [4620799, 82992]
3101 - [3932137435962837375, 70611885084286832]
3102 - [1093973, 19642]
3103 - [867667325140497045977, 15576230136070851324]
3104 - [76049, 1365]
3105 - [1236211536041, 22185130604]
3106 - [191448252305, 3435189348]
3107 - [876466774, 15724065]
3108 - [223, 4]
3109 [6211647661990218, 111402888773665] [77169133353417083138281455375049, 1383990987179785002726492017940]
3110 - [49346151679, 884857008]
3111 - [53560624, 960275]
3112 - [5964562960504723, 106919971197837]
3113 - [23067860999127, 413445020284]
3114 - [17299, 310]
3115 - [24178006, 433203]
3116 - [277795549080199, 4976529221910]
3117 - [49912994830590161975588599351, 894015868843226887123214940]
3118 - [89237584631512807552800143, 1598121342441062094523956]
3119 - [4301661990659037864538421520, 77024448015800300081493511]
3120 - [391, 7]
3121 [12605640, 225641] [317804319619201, 5688698430480]
3122 - [447, 8]
3123 - [641602, 11481]
3124 - [67606199, 1209570]
3125 [2360712083917682, 42229701559561] [11145923086309929722690704506249, 199384333543786067724288115204]
3126 - [1486438520792165, 26585967200418]
3127 - [403846704642599, 7221918828180]
3128 - [783, 14]
3129 - [895, 16]
3130 [17708464557, 316525525] [627179433933050412499, 11210362081696634850]
3131 - [85346621049, 1525263220]
3132 - [1567, 28]
3133 [12007987538529798018, 214530987128651245] [288383529450973834879765770615753456649, 5152170840138681288977055501228464820]
3134 - [3135, 56]
3135 - [56, 1]
3137 [56, 1] [6273, 112]
3138 - [3137, 56]
3139 - [415029507064295362010, 7407698821274160879]
3140 - [1569, 28]
3141 - [169648201, 3027020]
3142 - [669207511031237499832901, 11938718615110690961070]
3143 - [897, 16]
3144 - [785, 14]
3145 [1344783432, 23979605] [3616884957963397249, 64494751019808720]
3146 - [5517751251, 98374550]
3147 - [27921194970602, 497720615843]
3148 - [2397835852827853509127, 42736808590297163694]
3149 - [1248601441976935941472695, 22250383556353663872124]
3150 - [449, 8]
3151 - [47283258454664108425083440, 842331798900203480514057]
3152 - [393, 7]
3153 - [18970729627847767, 337848542050036]
3154 - [3419175201199711490262545, 60882224255870719804284]
3155 - [72854760249, 1297054580]
3156 - [16116667272575, 286884274248]
3157 - [88425666563849, 1573769235420]
3158 - [8213957, 146166]
3159 - [973051091875225, 17312541655556]
3160 - [6616066879, 117694548]
3161 [2298668, 40885] [10567749148449, 187962082360]
3162 - [62867, 1118]
3163 - [13829524802, 245899509]
3164 - [225, 4]
3165 - [6751, 120]
3166 - [614084477747659775, 10913716410016992]
3167 - [7717095408, 137129167]
3168 - [77617, 1379]
3169 [1356309863832314455774566238208011624500, 24093383896727483428141112399205123577] [3679152893457662761323580680295959204573920976260949003883472195854258000500001, 65356188464460261805058551772875990742920247280140668199515487179950041673000]
3170 [6137, 109] [75325539, 1337866]
3171 - [1856026465, 32959912]
3172 - [4393, 78]
3173 - [2413151, 42840]
3174 - [44716177445, 793708826]
3175 - [4730624, 83955]
3176 - [1828310451, 32442155]
3177 - [206333986213435088897, 3660683325992120448]
3178 - [1572054481606573, 27886284036474]
3179 - [250283080090, 4439011059]
3180 - [87807751, 1557110]
3181 [282, 5] [159049, 2820]
3182 - [80463946251, 1426432550]
3183 - [3533793124, 62635825]
3184 - [529178298454520220799, 9378113746817527740]
3185 - [8586369, 152144]
3186 - [258065, 4572]
3187 - [33518724973599159805322963185226, 593740205304452435439318600585]
3188 - [1221759532448649, 21638471501270]
3189 - [110897063235595249339381958198427895, 1963779787797964047747540004659996]
3190 - [50056379, 886266]
3191 - [2732882641389714120, 48379077178268683]
3192 - [113, 2]
3193 - [4053228630090230563044843848239999, 71730134036988504056228878450800]
3194 [4420459935979675, 78216792565273] [39080932091202864799204026211251, 691508395711244410187277652550]
3195 - [954809, 16892]
3196 - [359551, 6360]
3197 - [160127, 2832]
3198 - [65599, 1160]
3199 - [14583769822945, 257847355224]
3200 - [768398401, 13583493]
3201 - [9505, 168]
3202 [1641, 29] [5385763, 95178]
3203 - [3010285326252238226, 53189902261677345]
3204 - [500002000001, 8833351000]
3205 - [116874155559392009, 2064450476131524]
3206 - [134566757499, 2376599650]
3207 - [21975296167, 388047828]
3208 - [295496099, 5217165]
3209 [37274719969189347032, 658005510878888885] [2778809497562966152301116832629054418049, 49053942312387915305532411773665078640]
3210 - [5779, 102]
3211 - [170, 3]
3212 - [104430151, 1842630]
3213 - [3401, 60]
3214 - [2722742634151186538759112460772073211555627478218895, 48026800531883793826480891758974237154019847745804]
3215 - [122102241535124, 2153441846145]
3216 - [515095, 9083]
3217 [52726914523425161500370446879147776, 929622930226573693769864204943641] [5560255030321166451412373466331342083953713002443836653914008091492353, 98032297562145168108715817784342188210852197832334447264192380984832]
3218 - [389377, 6864]
3219 - [19574, 345]
3220 - [1514868641, 26696052]
3221 [25101291418, 442283465] [1260149661702720901449, 22203772288655606740]
3222 - [176579805797, 3110844242]
3223 - [218562859075276, 3849871290915]
3224 - [6166395, 108601]
3225 - [568182049, 10005128]
3226 [19370269996753830049557, 341038565390233978825] [750414719494283246397205120254318218151792499, 13212018181828836780205130200002950077261050]
3227 - [33358422, 587227]
3228 - [5375175144869407, 94607563270004]
3229 [7841692535790582, 137998951780205] [122984283651747456322071519797449, 2164290700243515993131946058620]
3230 - [341, 6]
3231 - [259199, 4560]
3232 - [778684942176337, 13697020335843]
3233 [1065376, 18737] [2270052042753, 39923900224]
3234 - [142771201, 2510560]
3235 - [8969825050006492148446, 157705496496673927983]
3236 - [376455160998025676163201, 6617729311231101255320]
3237 - [631605599, 11101320]
3238 - [333646757, 5863386]
3239 - [115402204680, 2027723021]
3240 - [27379, 481]
3241 - [25417969077448458815476572185794315237855, 446479302968989604177028852651508804392]
3242 [980539, 17221] [1922913461043, 33771724238]
3243 - [1082, 19]
3244 - [3820246930677755671933573219842576199, 67073506733999018168601507721042770]
3245 - [92511, 1624]
3246 - [2165, 38]
3247 - [3248, 57]
3248 - [57, 1]
3250 [57, 1] [6499, 114]
3251 - [3250, 57]
3252 - [2167, 38]
3253 [92682, 1625] [17179906249, 301216500]
3254 - [4910804185196699146565, 86088242748021944166]
3255 - [1084, 19]
3256 - [4206992174549, 73727499705]
3257 [416103175176838268, 7291084818881285] [346283704784493109167747146058479649, 6067687087240290895583870274028760]
3258 - [1045457, 18316]
3259 - [1204412859964726884213844443965680238889984046218177821690, 21097607271952384696890088342203142603326873550532163819]
3260 - [49074685471, 859505628]
3261 - [638642935, 11183628]
3262 - [20358143, 356448]
3263 - [36325223, 635916]
3264 - [49980001, 874825]
3265 [69193429690364472, 1210941783807937] [9575461424630823263024160399677569, 167578430354078047294555152828528]
3266 - [7214595, 126242]
3267 - [189750626, 3319775]
3268 - [343, 6]
3269 - [336700953497605016375, 5888936697884478036]
3270 - [9900251, 173130]
3271 - [1619748307207664426365321779196104474376957858283720, 28320913834308047704854247400637268662485889692637]
3272 - [40899, 715]
3273 - [8589741784055686372536599, 150143697253183208387540]
3274 [702702048110161293, 12280947698152505] [987580336836430872829983276950863699, 17259694200451072315048187323977930]
3275 - [225144199, 3934188]
3276 - [4954951, 86570]
3277 [7999189502401825182, 139735825449481925] [127974065390671119118297484409778666249, 2235546696089899238583819312637670700]
3278 - [31864843, 556554]
3279 - [635722350398965465, 11101886220126884]
3280 - [39689, 693]
3281 [1432, 25] [4101249, 71600]
3282 - [14792397377, 258207752]
3283 - [466058366908226, 8134013103255]
3284 - [9000987377460935993101449, 157068312726443201939870]
3285 - [1143905054699681, 19958242360056]
3286 - [2814651859822045595, 49101064282705422]
3287 - [172, 3]
3288 - [7397, 129]
3289 - [9688573605499877375, 168938217003261504]
3290 - [1848321, 32224]
3291 - [17679304830821210, 308177723658267]
3292 - [110610304532810910664294914294704844088447, 1927816418865777795062398139165666863368]
3293 [746, 13] [1113033, 19396]
3294 - [2993711291685588725, 52161265332452514]
3295 - [1769497877159, 30826366428]
3296 - [59535, 1037]
3297 - [4723844887, 82268988]
3298 - [161603, 2814]
3299 - [302737810995911463388788050, 5270787515411221348440849]
3300 - [48599, 846]
3301 [1603542558740706870, 27909864538036801] [5142697475385386685289187174530393801, 89509311190860097155540385627045740]
3302 - [16776447, 291952]
3303 - [19019995568, 330945229]
3304 - [222239304685, 3866347191]
3305 - [5289, 92]
3306 - [115, 2]
3307 - [104208463620296419822015562, 1812115585135932718393107]
3308 - [1622167924807, 28204152834]
3309 - [8309349191458434465841535, 144450359334108542937456]
3310 - [5430216369781, 94385034246]
3311 - [11239425, 195328]
3312 - [1151, 20]
3313 [1357511530935467298534271768858632, 23584833210518822858645209158665] [3685675113245512376543102238770368200726192730064006996280001822849, 64033366076938119044927701134973013709865177455727990600085692560]
3314 [1767145, 30697] [6245602902051, 108492100130]
3315 - [12494, 217]
3316 - [479835713751049, 8332691591130]
3317 - [71980098399, 1249797640]
3318 - [27649, 480]
3319 - [671622868694618180588582864545538521992490143004912760, 11657940896472359625043172719821996271285480583681739]
3320 - [146411, 2541]
3321 - [2368108374136006451201, 41092932594303413120]
3322 - [411003583823359999, 7130923784923200]
3323 - [585733464128762, 10160962912971]
3324 - [9799705, 169974]
3325 - [2588599, 44892]
3326 - [1494797672868137785177365350655, 25919181962970690309154678832]
3327 - [4650844441828, 80631625177]
3328 - [1419278889601, 24602321205]
3329 [22974395901623422122762860, 398187115544992467645737] [1055645734089062190249960388602447740969119590759201, 18296216870912253973171949333084823317324281855640]
3330 - [213859, 3706]
3331 - [3896641929395876391261634122890971172755584821846810, 67515452551331189136816152107604558605530293860977]
3332 - [9478657, 164208]
3333 - [3233, 56]
3334 - [236615826048429494541160021116112041696922702648911365765, 4097896556739353134495729190353304459906567382400709406]
3335 - [231, 4]
3336 - [6552578705, 113448622]
3337 - [998694953458090630415131953887, 17288398001052909929888104392]
3338 [3356579, 58097] [22533245166483, 390014340326]
3339 - [5746049, 99440]
3340 - [2357970660072459819271, 40800469770112229346]
3341 [12069218, 208805] [291332046263049, 5040226128980]
3342 - [388596986507, 6721964362]
3343 - [9959233904911272726432090224, 172249410447645778961383785]
3344 - [46551, 805]
3345 - [11213581593641, 193885926548]
3346 - [1734673949, 29988510]
3347 - [282187124940320162, 4877635451882313]
3348 - [12151, 210]
3349 [8429250, 145657] [142104511125001, 2455558534500]
3350 - [42588211249, 735812220]
3351 - [10116951813786265, 174768221838268]
3352 - [42112785797, 727381023]
3353 - [95745284209059341023, 1653486357184429176]
3354 - [16776449, 289680]
3355 - [744782306489, 12858286212]
3356 - [1411199, 24360]
3357 - [52387849, 904180]
3358 - [646530047, 11157024]
3359 - [1497900757074978480, 25845089375902831]
3360 - [1681, 29]
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3965 - [124929, 1984]
3966 - [2645, 42]
3967 - [3968, 63]
3968 - [63, 1]
3970 [63, 1] [7939, 126]
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3973 [125118, 1985] [31309027849, 496718460]
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3986 [670807, 10625] [899964062499, 14254648750]
3987 - [442, 7]
3988 - [14418057673, 228312234]
3989 [1115700250844450, 17665076095097] [2489574099468737305876191605001, 39417859660972040365509323300]
3990 - [379, 6]
3991 - [285984142932649574303357149060676, 4526901964409006077825213929315]
3992 - [984076901, 15575205]
3993 - [970614726270742103, 15360212398662916]
3994 [408916839388226966951390276246157, 6470397549647933907764628434765] [334425963070514018862720269408212980876968520550125856798514537299, 5291709031174723024227108953831224480295559459024277973512896210]
3995 - [71486, 1131]
3996 - [102688615, 1624462]
3997 - [92109151, 1456920]
3998 - [12925799920289343, 204425954517224]
3999 - [26876, 425]


[参考文献]


Last Update: 2005.06.12
H.Nakao

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