23^n=c mod n (2 <= n <= 10^10, 1 <= c <= 100) c | n ---+---------------------------------------------------------------------------- 1 | many 2 | 3, 7, 15, 2433, 38689, 787515 3 | 5, 526, 236618, 1609085, 51665926, 63110258 4 | 19, 287, 707, 5837, 7709, 42497, 3665753, 88504871, 286996619, 1538437757, 2230907441, 3121588379 5 | 262, 6081, 279836 6 | 17 7 | 58, 3306, 4475, 12035, 118315, 159475, 363774, 549797, 116383418, 148035882, 192448758, 212306378, 5609625239 8 | 9, 21, 45, 63, 105, 185, 579, 3789, 7299, 57985, 116067, 123207, 150723, 741699, 2362545, 2456577, 3016209, 7592781, 11587809, 40437285, 55884507, 57263753, 87805779, 171015345, 324636249, 342885845, 597757905, 601685385, 736610451, 889985673, 964814979, 1163912505, 1186348419, 1562658321, 2591195565, 2596211505, 3216003651, 4969052445 9 | 10, 26, 28, 70, 76, 104, 238, 344, 376, 1052, 1832, 2716, 7966, 11158, 13016, 18824, 26278, 62504, 102676, 104152, 138586, 158990, 183752, 234230, 426370, 430654, 471896, 473236, 499396, 656770, 686812, 726562, 732508, 832910, 2566670, 3218170, 3517819, 4313806, 4588690, 5005130, 5206033, 5491570, 13609544, 21447374, 28610996, 54606634, 63426970, 70055698, 103331852, 126220516, 150421096, 194672270, 214201256, 242674664, 344137610, 443393210, 514412194, 716927432, 746498066, 1077778822, 1128641618, 1257827012, 1552563796, 1688937256, 1702412719, 1774776136, 2720846158, 3769523390, 4544564888, 5098325368, 5616660344, 6241339048, 7433138984, 8901004168, 9039013490 ---+---------------------------------------------------------------------------- 10 | 13, 692887, 831181, 49655671, 1390646101, 1744407187 11 | 14, 74, 518, 969, 1799, 3039, 15869, 139286, 159026, 300218, 561507, 2006753, 2016437, 13410087, 44506133, 114187929 12 | 55, 19195, 3231635, 3309361, 46937029, 190474229, 633409733, 1193626027 13 | 86, 204, 678, 10364, 57444, 655026, 801516, 1661852, 3218165, 28066758, 2159002572 14 | 12153, 57706823 15 | 514, 11866, 14899, 335707 16 | 111823, 3260287, 3404825431 17 | 95, 215, 17195, 19076, 29595, 68902, 69956, 72195, 505895, 1665435, 3427408, 7611826, 17094992, 70738847, 97522409, 858242128, 6000829655 18 | 25, 245, 31829, 243383, 1123325, 1545425, 24994987, 73895087, 147673613, 279813569, 2152898153 19 | 30, 34, 90, 306, 906, 1062, 9210, 21786, 21990, 43830, 1068209, 1332726, 1351730, 11289666, 24857838, 102156770, 178563510, 323441658, 398022983, 436846794, 1231056791, 2497041306, 6975285810 ---+---------------------------------------------------------------------------- 20 | 12147, 683211 21 | 68, 254, 340, 1180, 3292, 829959380 22 | 235, 684715, 1145503 23 | any prime 24 | 280517, 1686001, 17953291, 79809781, 199334197 25 | 56, 102, 348, 356, 524, 646, 1074, 1316, 1416, 3576, 3638, 4408, 4548, 12162, 17768, 25512, 46802, 52968, 63012, 66434, 145524, 277694, 559672, 800934, 1171788, 2564238, 2658836, 8445418, 10209372, 14234339, 16629559, 17334868, 29777846, 51524184, 59697048, 63072296, 118352648, 166665864, 268733382, 305474154, 381741332, 618007352, 627204683, 865250598, 873728022, 1053369128, 2838813996, 3933051558, 5321145426, 5944367334 26 | 27, 57, 213, 15123, 23823, 32897, 806493, 1850047, 1931991, 28033001, 42222351, 87549321, 226816857 27 | 502, 19154, 4344022, 8045395, 37350982 28 | 16805, 64479229 29 | 51, 52, 130, 4867, 9178, 11507, 15897, 21524, 30597, 50579, 472353, 2243067, 2733843, 4539297, 9946276, 25279103, 30552047, 52068639, 122407719, 148805942, 215139183, 235548190, 766881937, 7187080803 ---+---------------------------------------------------------------------------- 30 | 49, 5971, 7987, 10759, 26593, 33229, 105763, 187811, 261131, 267841, 433699, 463687, 1286363, 4813879, 37182901, 59424421, 1264373459, 1283344279, 2198461783, 4976227931, 9803486479 31 | 166, 1686, 124226, 526818, 19763778, 1412311393, 2614919694, 4695169958 32 | 35, 75, 2427, 617713, 1532455, 3937575, 860961775, 3090171575 33 | 62, 136, 992, 4372, 35312, 54545, 213032, 569456, 896185, 3348244, 3348704, 4196944, 30100073, 49870445, 339423146, 351862465, 1151632136, 1657065692, 2716110482, 4624060328 34 | 1837, 95521, 66826853, 918026461 35 | 38, 387, 1011, 12429, 3324142, 7582779, 14861263, 17429897, 438992031 36 | 977969, 246799501, 3544912813 37 | 82, 426, 427, 492, 1162, 1692, 2044, 7542, 13324, 14842, 43132, 60066, 212148, 347502, 422524, 666383, 1512847, 5581681, 9704196, 10155146, 15721594, 21290972, 22837908, 31205604, 72709482, 73828782, 174803436, 2562368436 38 | 39, 933, 1405, 2545, 4965, 13767, 83499, 861627, 4723291, 35509389, 342206085, 652839073 39 | 1370, 2810, 3130, 4109, 3438010, 137252927, 350975366, 372749930, 596745170, 5628015730, 7186145170 ---+---------------------------------------------------------------------------- 40 | 289, 6326797, 1584149233 41 | 122, 129, 141, 3208, 5596, 11464, 27256, 1616998, 6384680, 14964501, 32213002, 77407964, 262645252, 1154354260, 5103353128, 6781899196 42 | (none under 10^10) 43 | 65, 5262, 24114, 24947, 44525, 366702, 1783525, 2252627, 3328817, 11826425, 61109978, 72693978, 92786291, 179592023 44 | 133, 1347, 12079, 6763011 45 | 697, 1517, 25436, 142796, 175516, 528902, 903962, 1570481, 3917497, 4913093, 5148979, 6777802, 12173753, 14087678, 128083822, 135698519, 247853353, 695538764, 1188591737, 1341443629, 1544368262, 2330910943, 2399536018, 3336846271, 5177804362 46 | 161, 713, 1081, 1337, 3366073, 7304593, 9355273, 10374791, 204682289, 2592889153, 2654244551, 6085429721 47 | 303, 482, 485169, 822502455, 4271741671 48 | 19445, 654551, 6676907 49 | 50, 114, 116, 150, 170, 268, 456, 2850, 6612, 8950, 9690, 12174, 19664, 22746, 24070, 27150, 34423, 40812, 43548, 44488, 48570, 66050, 69450, 81852, 87950, 104088, 143030, 222072, 236630, 255246, 276792, 279848, 318950, 373112, 418794, 515850, 528104, 547728, 727548, 793050, 891692, 1069710, 1099594, 1178070, 1947950, 2154738, 2991930, 3171991, 3219290, 3686190, 4168966, 4329768, 4577712, 9838412, 13387690, 13499950, 15833857, 17946150, 18678552, 20171856, 27456272, 35420730, 35615850, 41040850, 44954970, 45924496, 51591350, 63320028, 68018108, 77374690, 102289578, 123314090, 127438544, 133931144, 139203690, 158185032, 190485132, 222053844, 227859090, 232766836, 253265136, 294961434, 296071764, 384897516, 424612756, 491910778, 535376148, 601793232, 678294510, 817840272, 871602792, 1070820650, 1172407578, 1201516790, 1294186550, 1537003450, 1585768038, 1610889688, 1888117818, 2048647003, 2219195830, 2751900330, 3767184488, 4127704950, 4903359128, 5145032688, 5230770990, 5383334224, 5856099882, 6670490550, 7958953848, 9645824850 ---+---------------------------------------------------------------------------- 50 | 147, 1731, 2751, 188013, 25792347, 2574216141, 3287159463, 9757492077 51 | 259, 478, 146473, 769711 52 | 1247, 577361, 716213, 32181455, 544717255, 4698442855 53 | 452, 549, 783, 2019, 2476, 5249, 7263, 15363, 23841, 30285, 71309, 153245, 587865, 590301, 837143, 947068, 9826389, 18489742, 44421077, 109359603, 128618145, 232612436, 387180265, 484506466, 2448748673, 2539771965, 4784151365, 7105843233 54 | 551, 160921, 90608789 55 | 158, 834, 3002, 11394, 116894, 355002, 1454634, 21495821, 37981194, 54025967, 74857603, 226744457, 1215523314 56 | 143, 187, 767, 1101, 1177, 37109, 142571, 208417, 236291, 3967073, 20543423, 191297381, 343808223, 471441011, 2909175933, 3828879197 57 | 118, 164, 3412, 11567, 12175, 27875, 259475, 730168, 1425841, 2897078, 16090715, 79418104, 82143829, 129020201, 404316175, 1072498127, 1314413972, 1690142219 58 | 85, 378605, 10554229, 60834905, 143623913, 186021245, 3098429509, 3404825389 59 | 94, 3027, 19930, 302030, 688210, 1894107, 11581491, 16248003, 725111493 ---+---------------------------------------------------------------------------- 60 | 74351, 842177, 768831539, 2855171503 61 | 260, 4294, 6266, 6420, 7620, 9498, 16980, 18652, 46758, 326292, 2960220, 23162653, 56681140, 90450508, 112965738, 174490266, 201104740, 350082583, 956328308, 1569843804, 1637914940, 6165925932 62 | 153, 807, 963, 1791, 6137, 16735, 46503, 319283, 622761, 3114063, 19430835, 470389455, 1345900543, 1844963369, 2365716735, 7921876035 63 | 466, 3343867, 30849053, 34728145, 7399001845 64 | (none under 10^10) 65 | 112, 448, 464, 1479, 2023, 4996, 5866, 6051, 7504, 25192, 127808, 226496, 1255744, 1867312, 2113988, 3730552, 8847717, 33250808, 33380641, 47468576, 54123908, 75361196, 109162952, 209676741, 314521397, 680374729, 1019847831, 1223609144, 1446273472, 6606793888, 7415592982, 7866259721 66 | 118751539, 594366653 67 | 77, 98, 539, 959, 3678, 4169, 21954, 77315, 85998, 265782, 280543, 335258, 412819, 478489, 629258, 790769, 885082, 1059674, 1848539, 2536457, 2820893, 11438834, 18563243, 24410455, 78706397, 1325972755, 7644132078 68 | 111, 125, 285, 327, 3945, 4731, 7125, 11525, 12099, 49125, 361083, 429085, 499263, 850125, 58121165, 80158245, 90979125, 299221023, 394921365, 635991625, 667614723, 671645937 69 | 92, 230, 299, 3070, 12164, 18239, 19021, 30490, 57707, 203044, 522836, 962110, 2271572, 2727388, 8479778, 30346223, 128573519, 166010857, 332157421 ---+---------------------------------------------------------------------------- 70 | 40081, 5384957, 6713191987 71 | 458, 1071, 2373, 64323, 105901, 216741, 1588797, 4178853, 6733161, 13128591, 122361267, 127516989, 155618783, 2876436423 72 | 74881, 857437, 8278715, 27238603, 32181355, 289313177 73 | 222, 666, 13465, 46628, 49512, 111138, 267066, 1254665, 19831886, 24717816, 26792492, 45382794, 664623378, 886994748, 1970528562, 4235537252, 4392869304, 6735462156 74 | 87, 417, 1043, 24447, 28507, 55139, 115140063, 6571339759 75 | 454, 1807, 490711, 11262434, 3396502937 76 | 3910657, 51304727, 1895250607 77 | 93, 195, 226, 4215, 4953, 279764, 437572, 716235, 1461135, 4443387, 5363555, 6854835, 8021809, 11189015, 18481983, 100189372, 784132255, 7823762932 78 | 319, 15653, 141119, 361405, 1799743, 5494805, 35750627, 6597693905 79 | 390, 490, 890, 8722, 12570, 69013, 70691, 1217190, 2277474, 644225790 ---+---------------------------------------------------------------------------- 80 | 81, 237, 333, 711, 2133, 2997, 6399, 8769, 26109, 46953, 78921, 115587, 152181, 619569, 1650237, 1697301, 4529761, 34713743, 55855533, 57849093, 64377099, 101400687, 103419453, 205400007, 214934589, 215691093, 382999509, 393429717, 704216349, 2101800609, 7324414809 81 | 140, 152, 208, 232, 476, 520, 560, 688, 752, 1076, 1520, 1544, 1616, 2104, 3172, 3664, 5432, 6340, 7540, 7720, 11920, 15932, 22316, 22360, 26032, 27920, 37648, 38116, 52556, 76540, 78812, 84080, 100360, 125008, 131852, 182360, 205352, 208304, 228920, 234088, 254492, 263726, 272204, 277172, 291334, 317980, 319340, 330320, 331352, 367504, 448762, 468460, 468692, 557432, 568360, 708616, 852740, 861308, 943792, 946472, 998792, 1046260, 1095920, 1162360, 1292936, 1313540, 1373624, 1431476, 1453124, 1465016, 1474640, 1524596, 1641260, 1665820, 1702480, 1922480, 2011516, 2221688, 2260028, 2355652, 2382172, 2405416, 2655920, 3021460, 4968728, 5060072, 5133340, 6308972, 6436340, 6671624, 7035638, 7156708, 8399560, 8627612, 9177380, 9479708, 10010260, 10412066, 10575476, 10983140, 12792040, 12873172, 13811080, 14522840, 14700560, 14706680, 16293832, 17220938, 24416720, 24439480, 24980980, 25446320, 26344220, 27219088, 37102606, 42894748, 50513720, 54368888, 57221992, 63045452, 63558320, 64540616, 71155240, 72181720, 90007996, 100700752, 101263240, 104285392, 108608444, 109213268, 117584272, 122471720, 125159476, 126853940, 140111396, 180212336, 180639080, 206663704, 212017736, 214109840, 238555720, 252441032, 300842192, 309085640, 363156520, 368491256, 389344540, 397634384, 428402512, 465170120, 479405360, 485349328, 630368404, 672696532, 688275220, 728006192, 758693416, 759454468, 774893296, 783021680, 879700760, 886786420, 962012360, 1017143920, 1028824388, 1085444444, 1187559880, 1240570064, 1424545720, 1433854864, 1492996132, 1612244240, 2155557644, 2257283236, 2322781480, 2515654024, 2717318024, 2843297480, 2873756548, 2947923860, 3053272016, 3105127592, 3277055080, 3377874512, 3404825438, 3549552272, 3691689740, 3774342520, 3873657580, 4074827528, 4252785272, 4433846860, 4483338868, 4692612808, 5371161416, 5441692316, 5615020376, 5629703720, 5768328568, 5931590216, 6105502160, 6965381488, 7539046780, 7587026980, 9089129776, 9431922392, 9506392948 82 | 377, 475, 1157, 1175, 1781, 1843, 24401, 54275, 312055, 427895, 9862775, 12009775, 47867495, 51981775, 188206675, 188389175, 715842335 83 | 145, 159, 446, 685, 4611, 8265, 83687, 147117, 880365, 960105, 4418237, 4709739, 4925131, 15041085, 72255081, 97979745 84 | (none under 10^10) 85 | 1636, 2154, 5052, 15036, 29454, 83866, 192642, 822012, 3054468, 5007796, 24664578, 108556788, 158348651, 219391217, 531596708, 3524160734, 5270263068 86 | 12081, 5197447, 6493711487, 7831693927 87 | 695, 7235, 45266, 418409, 217137959 88 | 203, 47705, 203945, 309283, 1708637, 29157965, 68437087, 4829337317, 5762873417 89 | 99, 110, 183, 279, 3069, 3223, 4964, 36783, 53416, 165638, 176264, 802747, 884972, 2920863, 7426793, 36281876, 38399416, 75496388, 96705730, 241383490, 292519069, 882217730, 1078167926, 1391124703, 2640986307, 3791400910, 4849317110, 5708886381, 7119180472 ---+---------------------------------------------------------------------------- 90 | 92182997, 2697316289 91 | 146, 1206, 4247, 460386, 10193934, 12980718, 49345266, 652973058 92 | 115, 155, 295, 357, 483, 1173, 2415, 3255, 4767, 5359, 9047, 10695, 13461, 16895, 22323, 208311, 237909, 1090335, 1413695, 1702633, 2355599, 2491935, 6584555, 6895959, 8219495, 10319883, 16599261, 21476595, 27395777, 33022595, 34895427, 38831635, 47626467, 50325555, 54426855, 54657195, 56085477, 56495287, 70545237, 79100427, 133975317, 209593587, 359836995, 409036035, 466707467, 528849615, 895924955, 923056033, 1228881559, 1274473515, 1325022203, 1417769115, 2071269111, 2135117715, 3465599037, 3662565537, 6581401355, 9445272069 93 | 218, 388, 412, 3031, 25745, 118225, 139366, 145745, 232834, 1063174, 3931669, 7768025, 60476765, 681775025, 706613911 94 | 43205213 95 | 221, 1509, 1841, 384314, 565502, 1258649, 137015722, 889535762, 4043043641 96 | 50201 97 | 124, 188, 744, 904, 2136, 3232, 4512, 9224, 16696, 17484, 24432, 38497, 52895, 87544, 298544, 1008552, 1482882, 5001415, 10786912, 15661014, 15908512, 16090615, 18504474, 26848144, 27080484, 35805152, 106058184, 159304784, 194409168, 536008552, 844592204, 881994595, 1046710176, 2695124244, 8378963232, 9840863776 98 | 447, 1413, 160065, 580005, 605547, 20574693, 660369639, 2294461989, 5827563559 99 | 190, 361, 2830, 3610, 11510, 351950, 781831, 1338730, 6069290, 7984351, 10931878, 39336190, 88750450, 108537050, 2447695270 100 | 34573, 43409, 315271, 6020377, 1690953347, 2221953761, 3774575959 ----+---------------------------------------------------------------------------