83^n=c mod n (2 <= n <= 10^10, 1 <= c <= 100) c | n ---+---------------------------------------------------------------------------- 1 | many 2 | 3, 15, 114357, 2000935, 4552215, 2369938255 3 | 5, 22, 242, 626, 17182, 4588261, 8882399, 62125822, 165995302, 203338322 4 | 79, 4895129 5 | 13, 699, 796, 1227, 3442, 17116, 57941, 213473, 238484, 2556916, 1739602241 6 | 7, 11, 301, 2051, 5663, 5969, 495299, 2662331, 1513558081, 3426618197, 4624337641 7 | 19, 62, 74, 174, 475, 575, 635, 24546, 79675, 549581, 1456654, 2755758, 10556183, 28166981, 113709718, 520109869, 2074731961, 4000862519 8 | 9, 39, 45, 517, 543, 663, 1287, 49803, 110487, 343071, 488805, 906669, 1116429, 1429551, 6002805, 6107613, 8692527, 9736101, 10139721, 12070071, 13656645, 14487111, 19392087, 34274703, 40881161, 355606005, 370516887, 380092791, 951939087, 1313013545, 1714485331, 2192126865, 3382680465, 5625944145, 7109814765, 8270713905 9 | 10, 37, 44, 86, 370, 484, 790, 1252, 2794, 6644, 6892, 34364, 38296, 39656, 41624, 99604, 343108, 635734, 1499770, 5208386, 6738010, 6825710, 7652524, 8944804, 9176522, 17522998, 17764798, 21727954, 29092612, 61547510, 94916648, 124251644, 173320456, 203986732, 278323768, 331990604, 350645174, 356474138, 406676644, 422595230, 468624610, 553597423, 597054971, 599495608, 1309406818, 1431735868, 1964609128, 2183557244, 3153716164, 3862267132, 4364975054, 5475947608, 6731940424, 8257006504 ---+---------------------------------------------------------------------------- 10 | 73 11 | 38, 362, 4467, 103322, 4168851, 5923926761 12 | 71, 2495, 33115399, 181610603 13 | 102, 382, 642, 6313, 7268, 1656809, 10664994, 15819436, 23517349, 25323305, 89868162, 114683617, 264602532, 281360045, 640661219, 1821599204, 3392041622, 8870410313 14 | 23, 571773, 489597527 15 | 17, 982, 3827, 5942537, 18653527, 83087413, 232332394, 726187798, 1761637658, 4485941506 16 | 67, 5922583, 3556255063 17 | 995, 1072, 1718, 2056, 2115, 2455, 11121, 15179, 19059, 33239, 33595, 47403, 92692, 100017, 341895, 426501, 894328, 1012647, 12824937, 19554435, 39197176, 177485949, 410478344, 1201307248, 3009704895, 3715607848 18 | 25, 65, 325, 198185, 1917773, 4744045, 12656743, 709095545, 1319588465 19 | 30, 90, 458, 4530, 8310, 85730, 253627, 254677, 20260427, 74107290, 155970390, 292152319, 337330622, 2048630237, 2569595347, 4359204978 ---+---------------------------------------------------------------------------- 20 | 21, 57, 399, 2037, 2667, 4299, 12731, 13623, 19999, 24339, 50673, 278691, 337269, 496479, 1107519, 8751381, 32230821, 33903471, 87309579, 291655119, 351781213, 648082239, 1370843373, 2811026001, 3764480469, 6296775863, 8205542331 21 | 31, 34, 202, 20842, 46111, 72794, 1898332, 13427380, 8856902302 22 | 61, 2263, 2603983, 177905251, 1106629169 23 | 87, 93, 159, 6866, 758883, 53590126, 348317971, 818395077, 1184693618 24 | 59, 319, 365629, 65137259, 655415639 25 | 26, 29, 78, 132, 232, 344, 1247, 1398, 1532, 1592, 1608, 2262, 2454, 2724, 3048, 3102, 6884, 12412, 13332, 16494, 17284, 23892, 33618, 34232, 37362, 44063, 50744, 53461, 72312, 100644, 115882, 173238, 282838, 308386, 343452, 394052, 426946, 476968, 566196, 733062, 991932, 1049642, 1802236, 2116166, 2253124, 3563582, 5113832, 8181948, 9035938, 12599772, 15127836, 22341336, 31354264, 34183402, 35633494, 44716904, 121621686, 136060782, 150776886, 168818252, 210381826, 222489672, 237426566, 244734456, 553309198, 595466952, 1495007492, 1612217262, 1803865631, 1971722766, 2187834036, 2346564572, 2632300276, 3479204482, 3517095228, 3725225634, 3812589586, 4324606889, 4461043886, 5243488932, 8554602342 26 | 27, 51, 111, 303, 459, 7587, 9299, 58053, 3290113, 26116507, 2927294613, 6502082529 27 | 35, 94, 146, 15253, 17666, 1352186, 1581098, 15566803, 33098695, 4775540426, 6782295115 28 | 486211 29 | 33, 70, 92, 1610, 9716, 13843, 25989, 294772, 326470, 375886, 735574, 2631261, 3805089, 8635970, 45037412, 95938444, 955554110, 1916242259, 7515364198 ---+---------------------------------------------------------------------------- 30 | 53, 715553, 913349, 3983533, 9243677, 13749101, 59967101 31 | 254, 51486, 116077, 519018, 38100498, 56755654, 111863786, 430635414, 666689413 32 | 55, 75, 141, 275, 2433, 52895, 126775, 133815, 637575, 1936275, 3145175, 9604815, 10004675, 18142575, 22761075, 161661775, 185935695, 274048995, 380466075, 805152315, 969220615, 1300540775, 2668715097, 4532016975 33 | 68, 296, 536, 596, 824, 985, 1714, 4684, 4958, 21136, 2627452, 3035728, 5547992, 5857919, 9997565, 42534064, 52274636, 55295105, 130845808, 275651912, 343562873, 739148372, 1669848776, 4267259345, 7390330336 34 | 91, 299, 107737, 135623971, 706251091, 2426802287 35 | 46, 99, 298, 5517, 6957, 7941, 755829, 1292837249, 2241559107 36 | 47, 1853, 325583, 641392541 37 | 155, 198, 282, 404, 1142, 26604, 42906, 54042, 156628, 308692, 1385334, 2100366, 2101955, 3323935, 5784468, 24640835, 35373372, 310202076, 314421455, 323633508, 353919193, 2241529452 38 | 571749, 8155065, 57087545 39 | 274, 242290, 598080058, 3898986358 ---+---------------------------------------------------------------------------- 40 | 43, 106843 41 | 77, 214, 412, 40839, 46076, 62117, 210724, 493591, 1706920, 3386728, 4983297, 42562232, 58670373, 764638833, 5340982143 42 | 1343, 2501, 4715, 21607, 73531, 149035, 2361487, 2494235, 20384887, 53457037, 420427255, 612283495 43 | 326, 2225, 21126, 26725, 249666, 737825, 1122438, 2122049, 8672785, 28437394, 65658725, 157501662, 874417614, 1169030665 44 | 117, 207, 12077, 17057, 70859, 71669, 190581, 56169387, 100178487, 165427041, 1506519591 45 | 58, 76, 118, 2497804, 1800440833, 2027673502 46 | 69301, 2958989, 5017969, 3973717081 47 | 195, 555, 622, 2199, 2222, 3835, 7215, 26715, 355533, 391079, 10699455, 21744255, 23433455, 23764767, 24305255, 26906015, 81572803, 2195409434, 2770770795 48 | 49, 245, 36505, 594053, 27000911, 57420307, 221039245, 1507569967 49 | 50, 66, 124, 138, 148, 150, 152, 176, 348, 551, 678, 836, 893, 942, 944, 950, 1150, 1270, 1544, 1704, 1724, 3642, 4136, 5424, 5430, 5704, 5752, 6298, 7656, 8588, 11210, 14916, 17768, 18672, 21368, 21584, 32016, 37790, 38728, 38832, 49092, 55950, 58328, 62376, 68048, 69490, 77050, 96784, 103550, 114832, 159350, 161804, 168296, 185772, 188936, 240664, 291650, 324754, 408739, 468977, 627170, 859704, 1099162, 1125476, 1826544, 1911248, 2109038, 2913308, 2984330, 3335056, 3875434, 4077704, 4501410, 4909350, 5257136, 5511516, 6465930, 7368510, 9180116, 9514850, 9902706, 10398450, 11189708, 16779010, 21047356, 21112366, 22547310, 26525550, 26820596, 27024926, 35900070, 41896222, 49855202, 53919984, 55163370, 56333962, 61634276, 72017850, 77540170, 88636690, 103558024, 122521110, 123627650, 160179990, 165058476, 204611096, 227419436, 228354050, 261539864, 538919876, 557177828, 646556168, 669817896, 763931166, 789845828, 839672090, 869011116, 1040219738, 1057362568, 1247622990, 1255187576, 1347322290, 1365484144, 1387907288, 1457266704, 1642958416, 2336983850, 2342578984, 2696435832, 3178379910, 3494468316, 3601085732, 3634599538, 3743088810, 4149463922, 4229545036, 4257433576, 4880573850, 5053456050, 5393500850, 6418052408, 6742637050, 8001725038, 8355345358, 8517377616, 8894671896, 8952481712, 9670675150 ---+---------------------------------------------------------------------------- 50 | 571737, 37566331, 119730243, 567563541 51 | 526, 803, 6994, 32734, 48358159 52 | 3576947, 3780995 53 | 69, 85, 116, 765, 1333, 1924, 2236, 3105, 3418, 4143, 10305, 11444, 11596, 47014, 183285, 295677, 305187, 333045, 962323, 1321933, 1556307, 2792787, 4504874, 8417105, 12870322, 18217945, 38618045, 118027685, 129097852, 171343484, 284304645, 320737045, 429793142, 592062903, 957854092, 1908436246, 2191518164, 3148554753, 6384201165 54 | (none under 10^10) 55 | 134, 306, 721, 7902, 11538, 14178, 21522, 24678, 42246, 164563, 206334, 1167997, 2533847, 2801659, 18891341, 20948502, 1499244042, 2345497326, 3982050439, 4277499498, 5340639006 56 | 408839, 571731, 2383131 57 | 122, 775, 994, 2492, 5375, 18004, 32975, 42212, 94415, 109595, 167849, 270475, 484268, 539048, 836818, 3032081, 5108824, 5165194, 5997947, 29798804, 40279075, 120442988, 175547176, 191783449, 332602775, 361073275, 418998776, 611267129, 698140729, 879902324, 5869226375, 8265374404, 9784000675 58 | 6385, 524605, 788573 59 | 129, 831, 1366, 1510, 7599, 49258, 103071, 856511, 1142810, 1801322, 289145651, 330791378 ---+---------------------------------------------------------------------------- 60 | 731, 5083, 33371, 979133, 17484347, 2382548831 61 | 1138, 6180, 100734, 137166, 443748, 1054628, 2239620, 5790854, 7150614, 13256340, 101940260, 105795636, 127840380, 921063588, 1133354604, 2148619254 62 | 63, 315, 693, 915, 1719, 3015, 8295, 19215, 43155, 126135, 317835, 1561371, 6259515, 9988455, 12547395, 14220015, 20521095, 36295707, 69375411, 91515915, 194822019, 569321235, 1135278015, 8559347643 63 | 365, 6826, 12067, 13489865, 74426297, 180920645, 1696496941, 4517297129 64 | 33109 65 | 1706, 20288, 21872, 31736, 36087, 40952, 95552, 168496, 285861, 2551408, 6377872, 11247389, 11390864, 11864564, 13176544, 27455473, 27727928, 33069104, 336299896 66 | 3947877119 67 | 474, 758, 9606, 2584938, 83747255 68 | 125, 209, 759, 1805, 2945, 6665, 9825, 45125, 73625, 175085, 219773, 497837, 571719, 817545, 2472825, 8722625, 154167329, 234895025, 310392125, 472511625, 1073623025, 2063767299, 2435591279, 2454046025, 3040480185, 3148867625, 7617981125 69 | 18151, 135107, 211397, 271103, 618490, 928610, 11248070, 47458252, 74274470, 122733947, 7315647212 ---+---------------------------------------------------------------------------- 70 | 169, 221, 629, 7709, 2510117, 48317597, 56698823, 56830813, 81708289, 91842517, 160741477, 683038681, 877261013, 1520674909 71 | 518, 974, 1246, 1899, 3346, 7083, 18106, 29817, 47643, 259826, 390586, 563954, 3543638, 4253261, 6359711, 12484486, 84950163, 205831963, 941688994, 2878835259 72 | 671435, 2262055, 15781873 73 | 142, 143, 414, 488, 762, 5112, 8723, 14838, 14856, 22693, 29765, 33697, 41483, 43374, 75996, 81314, 330845, 1534122, 5697012, 7909708, 21736039, 66773064, 322721538, 519605676, 620970311, 895677086, 955341096 74 | 447, 3837, 23760627, 235024653 75 | 6814, 549514583, 7143505534 76 | 119, 371, 12719, 155561, 251167, 775019, 1762727, 3889543, 8657261, 9085236679 77 | 177, 244, 262, 268, 7855, 11612, 104554, 1126491, 1295781, 3759418, 5266515, 7156726, 22449435, 37539555, 110829244, 252521859, 264197674, 715568835 78 | 145, 52519, 546965, 135828985 79 | 426, 454, 590, 2910, 3090, 15294, 189510, 361302, 44342866, 59887290 ---+---------------------------------------------------------------------------- 80 | 81, 417, 1371, 16491, 881091, 2780293, 22764321, 2326941081 81 | 88, 172, 740, 968, 1580, 2320, 2504, 4360, 5588, 13288, 13784, 13796, 24056, 63220, 68728, 76592, 79312, 83248, 91024, 186980, 199208, 508052, 533240, 581276, 686216, 731534, 1271468, 1334596, 1513384, 1732880, 1919080, 2314414, 2908268, 2944460, 2999540, 3393808, 4624184, 4950502, 5704184, 6020240, 6428488, 6785768, 7718440, 8684594, 10416772, 12070264, 13476020, 13651420, 15305048, 17265320, 17889608, 18353044, 19368008, 20977958, 21901862, 23013880, 30825656, 32325604, 35045996, 35529596, 36644632, 37966664, 40212560, 43455908, 56082296, 58185224, 66651280, 82735928, 83123128, 83552696, 87699880, 94417720, 108620038, 123095020, 128802460, 141491108, 153268904, 189833296, 213500440, 248503288, 254281744, 258387496, 301983088, 346640912, 407973464, 431234408, 489346544, 491234860, 522890660, 556647536, 579249080, 599404376, 663981208, 701290348, 712948276, 720759248, 730404440, 748639720, 813353288, 831904406, 845190460, 937249220, 950009174, 954246760, 1106756680, 1107194846, 1194109942, 1198991216, 1270162168, 1646089808, 1695048560, 2618813636, 2863471736, 2868289360, 3014782640, 3362811248, 3742246288, 3929218256, 4367114488, 5739432688, 5900895640, 6307432328, 6380080654, 6471984880, 7596920216, 7724534264, 8729950108, 8918667496, 9927260428, 9939706753 82 | 2315, 9148921, 10890457, 14978791, 42538235, 44274775, 108924841, 536008015 83 | any prime 84 | 1266133 85 | 322, 826, 2422, 7908, 14154, 27426, 64596, 136074, 147102, 164094, 807506, 2259916, 3089618, 19211892, 20123436, 39512532, 70576842, 556725666, 1139878614, 5594205044 86 | 321, 411, 7037, 200281, 353851, 23195541, 90102311, 861035223 87 | 95, 358, 43871, 160598, 679253, 1385815, 25830815, 113691766, 160665395, 180040295, 1877865055 88 | 905, 80305 89 | 110, 170, 470, 2264, 2776, 2799, 5487, 10210, 10587, 22081, 200090, 880130, 5718290, 23729116, 92447337, 208936970, 292602357, 451986490, 4598623690, 4680776953, 4762976938 ---+---------------------------------------------------------------------------- 90 | 259, 469, 889, 1799, 32893, 289303, 335377, 63208987, 235428589, 1523278229, 7199742209 91 | 206, 562127, 5458913, 5952234, 23950762, 1757242337, 2704310179 92 | 5235, 114339, 14289293, 140590995, 192971055, 2693156055, 5417756935, 8020007315, 9392370495 93 | 506, 3398, 4471, 414436, 5879165, 7206389, 47458228, 193858604, 194988425, 1980682706 94 | 121, 21241, 122989, 970979, 923552531 95 | 158, 183, 213, 2013, 2162, 5183, 79563, 129063, 1373577, 1992766, 15097053, 674820113, 721367258 96 | 737, 54557, 112277 97 | 264, 372, 566, 712, 752, 3521, 3736, 4236, 5131, 5543, 8544, 13316, 31992, 68892, 109488, 386664, 465666, 650995, 692592, 710969, 1051421, 1053138, 1649632, 3432563, 4696176, 8988487, 9401818, 10350672, 11356602, 12440184, 170890428, 228084216, 258882184, 661611012, 668880928, 2257909912, 3996693572, 7848119712, 9035730097 98 | 165, 705, 190563, 595405, 16443585, 17778837, 927288391, 1219462677 99 | 194, 350, 490, 1778, 2450, 9506, 15274, 27650, 56459, 71582, 73411, 107450, 138670, 360290, 816550, 988330, 2677310, 3171254, 3665690, 5013047, 7764490, 17035550, 45051650, 62051431, 175846201, 339310850, 343970950, 405792730, 2839246186 100 | 194573, 32850817 ----+---------------------------------------------------------------------------