47^n=c mod n (2 <= n <= 10^10, 1 <= c <= 100) c | n ---+---------------------------------------------------------------------------- 1 | many 2 | 3, 5, 48885, 84963, 95631, 103821, 133885, 2956047, 3127413, 67109079, 315546645, 2096591109 3 | 11, 35, 121, 1169, 2206, 20086, 115415, 21824042, 1061784983, 1801466815, 3550634929, 4338396041 4 | 43, 192293, 31231973, 66083723, 98734063, 1984383463 5 | 7, 33, 38, 39, 58, 91, 143, 511, 1577, 3058, 200893, 829102, 851983, 940258, 4879676, 5040118, 5105243, 6704777, 7935121, 13187218, 88974907, 105969081, 512559723, 7590130822 6 | 41, 65911, 399457, 2203753 7 | 25, 734, 49442, 127019, 229345, 12186617, 44950025, 165909514, 8063292565 8 | 9, 13, 15, 117, 377, 2307, 24609, 146655, 254889, 286893, 311463, 345435, 401655, 622935, 8868141, 9382239, 33561819, 143248989, 201327237, 220029069, 244080695, 554605389, 946639935, 1191360735, 1460995497, 1824182169, 2095892835, 2379695979, 2487559149, 3749536557, 6199640415, 6289773327 9 | 10, 19, 22, 28, 70, 190, 242, 316, 532, 2338, 4412, 7928, 9848, 40172, 66902, 72952, 107932, 199670, 225910, 230830, 2459590, 4162202, 12070790, 19518712, 25689752, 43648084, 57096190, 65856472, 81908930, 120422092, 149186498, 153542587, 154599592, 377101690, 389578888, 478547356, 530466458, 558707816, 562496530, 707749832, 1044138502, 1121266910, 1351281052, 1681977682, 2123569966, 2169134926, 2402129188, 3203037784, 3602933630, 4477170907, 4878703496, 7101269858, 8676792082, 9382035518 ---+---------------------------------------------------------------------------- 10 | 37, 371, 2242717, 3303167, 11976461, 74159519, 120876329 11 | 14, 123, 314, 633, 1763, 15863, 165194, 455966, 1298602, 11277182, 17777038, 21353198, 71845593, 73923962, 701495606, 2292035402, 3860268794 12 | 385, 20849545, 112290805, 249164161, 670145353 13 | 17, 122, 764, 1037, 6702, 8516, 12932, 71436, 266204, 340188, 410261, 564132, 753253, 4825074, 8043521, 34489177, 66125442, 324272838, 352412873, 1360270493, 3673772951 14 | 39093, 103809, 55453431 15 | 2194, 23112101, 28776974 16 | 31 17 | 45, 152, 203, 219, 237, 274, 445, 665, 1208, 8765, 62027, 444464, 681104, 1041113, 1219916, 1290105, 1559013, 1729763, 2120133, 2300123, 21394133, 34579772, 935263768, 4149753688, 4436857785, 8373740464 18 | 29, 41215, 139115, 2664215, 3669275, 24462815 19 | 30, 49, 90, 146, 343, 642, 1362, 11263, 13590, 29586, 43830, 46001, 200449, 390062, 2829377, 3663221, 20307990, 42619870, 57449646, 629949402, 3045965814, 4113819230, 4779658009, 5526991026, 5635731390, 6132636078 ---+---------------------------------------------------------------------------- 20 | 21, 14829, 262200477, 4092890649 21 | 731, 1076, 1094, 3628, 39262, 139373, 330881, 354548, 2838860, 24193273 22 | 2460569, 20324533, 62577883, 229344985 23 | 55, 519, 2186, 11715, 24503, 76715, 254217, 93060335, 185051794, 257057715 24 | 161, 2177, 3013, 3841, 1829471, 4196741, 142366259, 425692349, 3639433223 25 | 26, 56, 66, 76, 78, 116, 164, 182, 286, 606, 1022, 1106, 1542, 1784, 3154, 3302, 4168, 4344, 6116, 8242, 11341, 14588, 21108, 24414, 25298, 174696, 264668, 324884, 401786, 586586, 715962, 1162106, 1203796, 1658204, 1703966, 1880516, 3050806, 3552038, 3557672, 3637686, 3885224, 4073366, 4178674, 9121668, 9759352, 10080236, 10210486, 11059646, 11664984, 12231706, 13409554, 15870242, 16549442, 17908836, 18384108, 26374436, 27510926, 34015818, 36682646, 58587288, 72368904, 81845304, 86876808, 120893146, 130717262, 177949814, 211938162, 212907594, 260179998, 280116746, 390067656, 409019602, 428118594, 1025119446, 1199729044, 1227287282, 1424708058, 1436832982, 2022741446, 2052002456, 2544797028, 2772804998, 2790253411, 3640287434, 3779512854, 5978753386, 6474741956, 6519508948, 8191207848, 8997180456, 9027819228 26 | 27, 57, 99, 469, 1233, 1821, 17479, 92739, 123519, 247049, 266829, 12983949, 18526519, 34413529, 298895653, 554084001, 1147906089, 2052899517, 2859469081 27 | 205, 2182, 15763, 491018, 546073, 1398445, 133611698, 5673693698 28 | 361, 395, 5881541599 29 | 218, 51897, 1662844, 4879652, 6628190, 1789712356, 4207044727 ---+---------------------------------------------------------------------------- 30 | 6663964249 31 | 77, 1507, 7007, 7282, 17142, 119147, 2363593, 3772914, 2599850141, 5668402598 32 | 87, 465, 2325, 3579, 38905, 117025, 148965, 242481, 244425, 519105, 669425, 1130345, 1144905, 1407085, 3426585, 7047925, 15637065, 18859119, 26619805, 41991825, 83478167, 172289225, 290122025, 313275925, 1577733225, 2278677165, 8685501945 33 | 34, 124, 1054, 1829, 6499, 7483, 8744, 19676, 25808, 103354, 139279, 182086, 1868128, 63386995, 68990395, 89999593, 138723502, 551904194, 573362435, 607338022, 664063702, 1771672646, 4270739095, 5446314424 34 | 639199873 35 | 93, 2174, 43646, 70047, 1180917, 8286129, 25258826, 368386001, 518109429, 592783798, 812088142, 1548568823, 2132278191, 4439194978, 5213319781, 6682500718 36 | (none under 10^10) 37 | 44, 154, 362, 11034, 21124, 28734, 41682, 64724, 355222, 4452996, 4821082, 12377766, 29024026, 114672485, 1162622924 38 | 51, 111, 119, 255, 555, 867, 955, 1883, 1887, 4335, 9435, 10115, 12215, 14195, 22755, 24395, 32079, 37655, 48671, 160395, 214635, 285895, 386835, 526235, 1183931, 3413883, 3617823, 6576195, 10152995, 10443315, 12225567, 14159555, 17802735, 24853371, 26528435, 94786815, 108700635, 359398955, 429660431, 2538421593 39 | 62, 8587, 28582, 185990, 349390, 430178, 8357839826 ---+---------------------------------------------------------------------------- 40 | 45301, 67831, 9121591, 373204057 41 | 172, 542, 609, 1059, 11348, 17661, 29620, 36776, 233458, 6793131, 7251909, 9557720, 418831833, 1035948952, 1434889659, 7348302482 42 | 69331057, 229344965 43 | 551, 1535, 81222, 113754, 933815, 872544157, 3183169074 44 | 247, 1359, 2661, 537147, 647667, 4285881, 102989871, 1461808017, 4150407027, 9277140529 45 | 1082, 104939, 311989, 1250798, 4879636, 5552198, 23745242, 76708076, 104997902 46 | (none under 10^10) 47 | any prime 48 | 319, 48115, 1825555, 23033161 49 | 50, 88, 114, 150, 456, 528, 568, 848, 1108, 1392, 1468, 1793, 2190, 2384, 2508, 2850, 3352, 3828, 4098, 4390, 5176, 5430, 10586, 17958, 20766, 31658, 33198, 46950, 47350, 47676, 57296, 86286, 95024, 98884, 104588, 111950, 128784, 170088, 199252, 217968, 254038, 287472, 380076, 396390, 410950, 458690, 635550, 737808, 759308, 769224, 870710, 1187538, 1852386, 2911128, 2985616, 3844536, 3876350, 3877168, 6760303, 7962438, 8658150, 9715278, 10799448, 13282588, 14909430, 15590184, 19125096, 19126392, 24373234, 28434416, 28919318, 30661872, 39543932, 40472912, 41718984, 45875850, 47253228, 51864978, 59814512, 65864072, 84820868, 89900050, 123044874, 124070070, 125628630, 133583430, 241166838, 263479890, 272827038, 295168344, 313291932, 322119248, 331819028, 387001298, 388866936, 406551612, 426803430, 581472730, 613610310, 665171492, 754098668, 836617170, 841640008, 889755450, 996719664, 1045189050, 1149798630, 1159287050, 1202156950, 1255745604, 1424907696, 1456836788, 1604056236, 1898355696, 1939597070, 2735620464, 2760152312, 2890951152, 3530468850, 3943262348, 4097027650, 4202332184, 4967914344, 5101305198, 5394632078, 6064233648, 6287141708, 7060193474, 7077163350, 7462682490, 8900144670 ---+---------------------------------------------------------------------------- 50 | 103773, 125911923, 5004064061, 9947587029 51 | 166, 826, 3514, 10034, 8911810319 52 | 581, 330079 53 | 135, 297, 428, 572, 1107, 2817, 3459, 3508, 4642, 7574, 30339, 48107, 147855, 175238, 1058246, 1546076, 1813574, 2278503, 2439621, 7214643, 7912268, 27964036, 35610327, 43639955, 52697204, 59690582, 84722667, 176777253, 191120795, 383627086, 391777213, 706823884, 2954707515, 3072463353 54 | 135847967 55 | 323, 718, 2022, 20142, 6226674, 10661934, 3275216766, 3495939199, 6636501082 56 | 31929, 103767, 9625709 57 | 125, 538, 2908, 3356, 222665, 4169864, 14941625, 40161304, 256723045, 379701736, 386656762, 420772171, 1381561939 58 | 163361, 382853, 1059091, 3641030047 59 | 86, 25941, 125573, 239570, 532310, 650246, 838479, 41245970, 257797490 ---+---------------------------------------------------------------------------- 60 | 3883, 15983, 3091769, 13441703, 250052171, 964343861, 1089148643, 7700333083 61 | 133, 358, 21074, 108436, 147786, 218814, 360858, 503881, 1668751, 147385740, 187248020, 292339380 62 | 63, 105, 183, 549, 1281, 2165, 2745, 3843, 4221, 6405, 21189, 25845, 322605, 3126921, 6462645, 11710377, 18493797, 29956185, 127979037, 339945341, 392607285, 637489377, 701584485, 712407471, 1779102885, 5025526965 63 | 74, 155, 1682, 2627, 5735, 55463, 1137935, 13092746, 628217015, 2830471282, 5646310667 64 | (none under 10^10) 65 | 112, 134, 448, 1556, 12736, 51879, 73097, 200066, 996896, 8742688, 11534384, 16056416, 17746544, 26489696, 34054336, 71737918, 123734841, 816465748, 2805940041, 3506702272, 9050670496 66 | 497, 959, 9083, 778411, 1530751, 364589477, 3915588613 67 | 98, 102, 174, 986, 1146, 3365, 5894, 7745, 34691, 34714, 43826, 71885, 114474, 245922, 304205, 1344738, 13592939, 32253114, 32328926, 39342386, 84276131, 103024382, 257746758, 1413448685, 1647982985, 4838189766 68 | 75, 175, 375, 3021, 5415, 6515, 19155, 20751, 34531, 41675, 135375, 367843, 978103, 4638057, 5864875, 15582175, 21422823, 806381223, 1957025375, 2959197695, 7145033875 69 | 214, 292, 451, 3932, 113492, 330919, 732502, 984554, 2386516, 15978971, 30396476, 529618771, 4960700284 ---+---------------------------------------------------------------------------- 70 | 299, 1859, 2323, 3887, 14339, 40141, 84383, 159367, 4849547, 2627356979 71 | 393, 638, 2138, 3012939, 32088971, 277981083, 417871647, 2715386278, 4681306594 72 | 692885, 1135153 73 | 95, 178, 1673, 1704, 2984, 8015, 11435, 14856, 29556, 32484, 43715, 46758, 115266, 195377, 308376, 813268, 3275352, 3957732, 10384202, 83311398, 147351426, 354382584, 729143567, 1483833407, 2393936724, 7008255217, 7770949574 74 | 3401, 24263, 103749, 271904641 75 | 194, 3047, 654026, 161539147, 456798287, 587694382, 1108122602, 1199549789, 2262653557 76 | 265553, 398399, 1171603, 566221307, 2679398653 77 | 82, 212, 16042, 16059, 51873, 92068, 135111, 2217387, 10889457, 12741385, 19169588, 106495766, 542112302, 1033276359, 1867009468, 2432534716 78 | 215, 1500949, 9799295 79 | 142, 490, 3786, 19970, 23170, 136662, 13251811, 64330194, 255165769, 273639770, 717925894, 1019696190, 5214832698, 6232692430, 6593404674 ---+---------------------------------------------------------------------------- 80 | 81, 801, 891, 6713, 34581, 54761, 167103, 674093, 1037877, 1693791, 5097741, 7953071, 10609731, 273114477, 2121816759 81 | 140, 209, 380, 484, 560, 632, 820, 1064, 1160, 1576, 1694, 4436, 4676, 8588, 8824, 10640, 15856, 16360, 16604, 17840, 19696, 19816, 20558, 34480, 64360, 80344, 118120, 133804, 145904, 215864, 266456, 322949, 323120, 399340, 451820, 458768, 461660, 572558, 1022960, 1075720, 1124464, 1302980, 1358740, 2647802, 3574280, 3656959, 3802328, 4077332, 4919180, 6644228, 8155280, 8324404, 13310044, 18243344, 18281240, 21117848, 22276520, 24141580, 32031760, 34806506, 35983472, 39037424, 50604188, 51379504, 53491088, 60818948, 62509744, 75369980, 80155052, 81766280, 87028382, 87296168, 90326416, 94649104, 101136560, 112660478, 114192380, 114581672, 131712944, 139910960, 150488240, 163817860, 177308392, 182580104, 226826869, 240844184, 253217180, 258918086, 263202764, 298372996, 307085174, 309199184, 336283880, 346509860, 362068784, 375659312, 384605093, 424713332, 450400688, 718650320, 746550686, 754203380, 759271004, 779157776, 957094712, 990100580, 1060932916, 1117415632, 1123386920, 1124993060, 1348010480, 1415499664, 1419614264, 1466602052, 1548225980, 1607257040, 1687299338, 1771919140, 1958060684, 2088277004, 2242533820, 2597203720, 2702562104, 2813567602, 3363955364, 3549288692, 4011619120, 4247139932, 4338269852, 4804258376, 5557202840, 6406075568, 6615598172, 7205867260, 7517007880, 7642461080, 8758243304, 8954341814, 9121773080, 9485106320, 9757406992 82 | 3325, 76621, 9986725, 45868985, 156358825, 901714741 83 | 195, 399, 2126, 5187, 15163, 73411, 83135, 880995, 1152255, 5109195, 9886155, 49880415, 93315963, 112791315, 140901663, 228935847, 1913579661, 3598605213, 4036144917 84 | 4228544597 85 | 118, 20388, 55524, 88597, 1626532, 2218188, 8352514, 9981636, 29806516, 221505598, 769943946, 1355784029 86 | 453, 687, 59037, 881499, 2769771, 3268317, 5119413, 59643753, 81334929, 6170579493 87 | 1385, 1505, 2122, 14785, 1139285, 37345342, 115343333, 3579439882 88 | 5155, 76232711 89 | 106, 110, 339, 584, 872, 908, 1393, 1479, 4879, 6307, 10210, 10251, 10748, 33439, 267110, 269479, 849507, 1635370, 1906714, 6978290, 9303279, 34272370, 38367759, 43833890, 87241399, 177297327, 241997291, 2992495496, 3059631297 ---+---------------------------------------------------------------------------- 90 | (none under 10^10) 91 | 522, 706, 1206, 8682, 20526, 45426, 75246, 26269937, 31975458, 234620166 92 | 213, 1461, 1985, 19999901, 543969019, 3237724407 93 | 115, 253, 322, 575, 2615, 13453, 17963, 20818, 30308, 34046, 90436, 287975, 378028, 3489275, 6405742, 7642946, 11356543, 13429933, 46525412, 79183313, 89340878, 235562228, 240013018, 260272738, 426415975, 768703135, 2742527495, 4785000638, 6496331255 94 | 329, 159377, 1620558809, 5910515921 95 | 302, 434, 6483, 71878, 1451198, 33380614, 158461167, 769159474, 3266691411 96 | 4667, 328747, 2513953351, 8454483791 97 | 132, 248, 258, 352, 636, 948, 1488, 2064, 3488, 3704, 6352, 13548, 14047, 15308, 21328, 24144, 38804, 50244, 50892, 54744, 67772, 88139, 157728, 194288, 235896, 256944, 334163, 527032, 1726944, 3916866, 4143192, 5377592, 12954373, 24279504, 32777744, 52934768, 65860716, 72528158, 115102938, 138248024, 147162768, 175076572, 190240145, 936688836, 1263727688, 2564359463, 2594439782, 7595216112, 9645196098 98 | 153, 435, 1383, 48501, 127553, 1322635, 2665617, 94715895, 297659273, 2478965789, 6721677549, 8849498415 99 | 169, 422, 1157, 61009, 86230, 776938, 3873950, 4224950, 5482573, 14588974, 24967843, 174387650, 354320837, 484529146, 909463970, 1134822994, 4143722578 100 | 856883 ----+---------------------------------------------------------------------------