13^n=c mod n (2 <= n <= 10^10, 1 <= c <= 100) c | n ---+---------------------------------------------------------------------------- 1 | many 2 | 11, 140711, 863101, 1856455, 115602923 3 | 5, 166, 287603, 9241538, 2366680105, 8347156585 4 | 51, 129, 125869, 158287, 1723647, 1839003, 90808797, 3661886147, 7368982721 5 | 44, 82, 236, 25433, 177764, 219244, 86150213, 107218402, 1260236441 6 | 7, 8743, 50239, 312389, 8789977, 87453889, 96301009, 3963715129, 5062673539 7 | 15, 75, 219, 1335, 3246, 4975, 5475, 7775, 8922, 28614, 67675, 69998, 103135, 313609, 548983, 624193, 6539595, 13193562, 26383395, 111892866, 315953675, 5330142066 8 | 371285, 3957661 9 | 10, 172, 296, 332, 410, 872, 1048, 1070, 1544, 2830, 3470, 7486, 9196, 22184, 90892, 121174, 299816, 575206, 885112, 1329388, 1386430, 2518994, 4167272, 5600212, 8475016, 9180370, 12348446, 18483076, 19185890, 20806274, 28984094, 37114141, 47809990, 49019830, 49914152, 101794376, 149023606, 386192518, 587105548, 621617656, 948117896, 1333829710, 1797455176, 1908624728, 2721757016, 2897753528, 4026049774, 4733360210, 6153775690, 8911490716 ---+---------------------------------------------------------------------------- 10 | 74853, 1275039, 27181907, 31261887, 989255061, 4813809711 11 | 158, 301823, 1851103, 8616098, 60528467, 1087582634, 1628818307 12 | 13757837, 6969969233 13 | any prime 14 | 5805311, 392908759 15 | 22, 1582, 11266, 52766, 76202, 100562, 494371, 641141, 1698494, 66593158, 469296521 16 | 2181, 13803 17 | 38, 892, 4595, 19532, 33896, 39388, 65264, 146399, 160646, 220481, 564272, 9703156, 74061779, 85745488, 220455628, 407865352, 692672132, 969742762, 1823555152, 3113741164, 4625635568, 8322875734 18 | 25, 11472673, 772289423 19 | 30, 33, 90, 354, 606, 5634, 13590, 191493, 249201, 345717, 1111606, 2958090, 5273454, 10473903, 14611659, 16076682, 16124646, 24289110, 730681353, 8383382610, 9904650090 ---+---------------------------------------------------------------------------- 20 | 9667, 45437, 339623, 2850257633 21 | 74, 2540, 5708, 39287, 121460, 130954, 788594, 64319642, 112575962, 496740364, 3422592956, 3911977442 22 | 87, 2929, 1027198855, 5510997007 23 | 146, 685, 15989, 294643, 31718723, 74332319, 3727600439, 7980459874 24 | 23441, 36565001 25 | 88, 116, 164, 184, 472, 543, 804, 822, 1738, 2202, 21484, 24978, 32314, 50866, 83498, 144084, 355528, 386628, 401944, 438488, 488534, 1007124, 1252658, 1264674, 2007678, 2110098, 2245317, 2760284, 3911736, 5335628, 6068568, 7855468, 8123228, 13644964, 14480412, 20713078, 28383828, 28803416, 33300044, 34081858, 49603928, 61894668, 83511942, 116539068, 123386766, 172300426, 198417144, 214436804, 221504014, 244537404, 255281612, 305797236, 365340028, 386435692, 407041764, 412848678, 413559438, 417644788, 588039708, 640653868, 832685673, 857656104, 1160321466, 1325279378, 1425429067, 1638168072, 1890822098, 2520472882, 3206401078, 4013832232, 4094883354, 4161472284, 4611467272, 8486252148, 8772597228, 8779070472, 9414057446 26 | 19629779, 55185121 27 | 35, 115, 142, 1435, 5173, 8491, 26635, 603728335, 1485399601, 2245175234, 4384328387 28 | 45, 99, 265, 723, 2619, 4077, 70883, 1949205, 7141077, 9031689, 236507853, 350549505, 405204899 29 | 70, 644, 1162, 4076, 107170, 1001644, 1571710, 56271868, 8165321332, 9847035130 ---+---------------------------------------------------------------------------- 30 | 235433, 738683, 21357359 31 | 46, 57, 66, 32846, 438798, 2295577, 5614026, 22247779, 123624507, 204741458, 331419898, 668822197, 945224149, 979265621 32 | 55, 275, 20401, 24775, 168755, 703555, 967835, 9282275, 24247477, 29782775, 414409435, 440906255, 578014615, 834525175, 4465141075 33 | 34, 4885, 7132, 14752, 18208, 1047113, 1214243, 1593224, 6627518, 30451888, 90440723, 135350158, 151992992, 224596432, 258139198, 331898824, 3028790822, 3056762348, 3122118239, 7027150397 34 | 309, 407479, 7076181, 20916161, 23780407, 44773379, 67891649, 147196407, 2191939669 35 | 134, 451, 1572566, 5863451, 6387034, 10614571, 18226358 36 | (none under 10^10) 37 | 132, 155, 171, 855, 2495, 4215, 9508, 10755, 11835, 85329, 240255, 752532, 804462, 1600302, 1934262, 6999462, 8309862, 12217566, 12570244, 36500662, 65477852, 69766443, 126332802, 293897181, 3377797002, 7191293316 38 | 205, 4031, 18245, 49405, 6016079, 31803085, 432579943, 505734683, 737118457, 8417646245 39 | 130, 230, 670, 1066, 8242, 39479, 102710, 122473, 240409, 869219, 4895410, 624372071, 1073417018, 2244189083 ---+---------------------------------------------------------------------------- 40 | 2157, 31867, 276329, 517761497, 1203491651, 1586505057 41 | 92, 124, 917, 35687, 92662, 119749, 196760, 266540, 502532, 544580, 560302, 2950072, 9654454, 136426474, 163146136, 189839420, 389830391, 501160033, 584835052, 1078379449, 5619145036 42 | 1856255, 96108451 43 | 165, 246, 266, 825, 1077, 16818, 133485, 366825, 520422, 580342, 7597425, 30760086, 36809394, 173850825, 185154214, 277169365, 789122211, 1182026229, 2227809459 44 | 170719, 345991, 12382897 45 | 62, 11222, 28516, 5235058, 6352757, 6692911, 90674524, 100493387, 9490672657 46 | 717, 1611, 59243013, 613195551 47 | 122, 895, 901, 1037, 5063, 122534, 14547713, 23631095, 46048595, 175386166, 510743423, 1542710618, 6949462643 48 | 49, 133, 245, 2009, 471793, 753767, 85427405, 496582765, 817749865, 1215264043, 2893647085, 4976126105 49 | 50, 114, 150, 174, 264, 438, 456, 470, 496, 537, 636, 790, 1392, 1416, 1808, 2670, 2850, 5352, 6492, 7608, 9950, 10950, 11086, 13110, 15550, 16050, 16188, 17076, 17844, 19928, 28568, 37992, 38072, 51819, 54858, 57228, 63510, 64024, 96286, 103056, 119732, 135350, 139996, 206270, 229616, 230073, 281950, 352024, 408950, 546870, 575070, 582152, 627218, 670690, 686508, 707550, 918928, 971408, 1097966, 1130478, 1248386, 1284666, 1609224, 1883850, 1951224, 2020836, 2337592, 2454990, 3246550, 3879510, 4437208, 4819028, 6089424, 6461554, 7516248, 7592374, 11023510, 12662184, 13079190, 14437712, 16070872, 17675544, 23390128, 26286907, 26387124, 32653724, 43583910, 52766790, 62397392, 63993786, 82389966, 94189650, 108244046, 144664376, 148291350, 155732550, 187367550, 195740592, 208605032, 223785732, 251529648, 256048944, 281994448, 329898796, 355850814, 356456112, 364910744, 372794712, 461934150, 466995450, 476779466, 558926150, 564967824, 631907350, 634335504, 676969890, 701610402, 843147850, 948524712, 1064957968, 1204669884, 1207802049, 1215940548, 1462793142, 1622408358, 1795939050, 1896076158, 2799842622, 2961512350, 2971842288, 3075070542, 4384308606, 4723026270, 4862652436, 5224413414, 5390947470, 6060148422, 7367919326 ---+---------------------------------------------------------------------------- 50 | 5775719 51 | 118, 23617, 52146127 52 | 95, 143, 195, 533, 835, 897, 2235, 2453, 2769, 3435, 4173, 4687, 9195, 13143, 17329, 57993, 107133, 145613, 161479, 172861, 300553, 318755, 748803, 770433, 1530451, 1740453, 2274355, 2636895, 3233269, 3943979, 7081581, 12130835, 20027453, 30740303, 39154323, 40807455, 86157223, 117375915, 149266347, 153709959, 211510149, 251756895, 303728815, 357476163, 447952453, 512837193, 1267396635, 1446375297, 1736366601, 1822370173, 1828845813, 2687753315, 2691639561, 2834037067, 3300090963, 3823089303, 6890109573, 7847158033, 9105795367 53 | 58, 1276, 10076, 28508, 46405, 545722, 5062042, 8898626, 167766637, 2619483638, 8284791371 54 | (none under 10^10) 55 | 63, 119, 161, 189, 414, 459, 1071, 1251, 4431, 8337, 8589, 26747, 42563, 82089, 103887, 107433, 272754, 399483, 893571, 1466802, 1480139, 1608918, 1816461, 2417111, 2455913, 2585331, 4536399, 17019471, 18746427, 39822867, 450159471, 995657643, 1037780067, 1052725194, 1152706947, 1755709731, 2731834579, 3183633747 56 | 39271, 2319949, 2622046477 57 | 775, 1988, 2036, 2044, 2152, 5992, 12556, 166684, 433208, 445327, 720823, 861644, 995875, 1247875, 11457895, 180780844, 1413920023, 2709105112 58 | 69, 93, 123745, 197985, 13541907, 50400951, 369815153 59 | (none under 10^10) ---+---------------------------------------------------------------------------- 60 | 36289597 61 | 76, 267, 1446, 1786, 2748, 4236, 5206, 6180, 10014, 17180, 23406, 112620, 275460, 791998, 1340454, 57642132, 298031380, 607168932 62 | 77, 2443, 3269, 51253, 181357, 603635, 1199249, 59686981 63 | 106, 11171794, 12770585, 83032867 64 | 153, 237, 387, 2193, 3033, 36279, 43047, 57069, 130419, 265203, 377607, 474861, 598893, 739041, 1489203, 3311481, 4696981, 5170941, 5361177, 5517009, 6914493, 10286337, 14686317, 15176121, 43675407, 52240743, 70685913, 71619237, 272426391, 575635791, 3759608973, 5233670997 65 | 104, 208, 416, 548, 832, 962, 1508, 3632, 12064, 21088, 21944, 31168, 37843, 55744, 69056, 143392, 158132, 226928, 308954, 565442, 2118857, 3056576, 3115424, 7730593, 15687128, 16349008, 150263737, 158651744, 280866703, 386447296, 464563723, 471811288, 1097604941, 1163638514, 3021947942, 3745489744, 4169715394 66 | 14961601, 155955859 67 | 102, 213, 474, 1258, 1927, 3594, 4843, 14314, 89998, 309355, 2801334, 52352854, 118999198, 155098582, 3687731018, 3746804574 68 | 125, 107591, 1578181 69 | 259, 469, 748, 791, 1676, 2108, 4964, 15436, 26044, 29308, 101618, 6549964, 6633332, 25256794, 45968531, 340544908, 3477322906 ---+---------------------------------------------------------------------------- 70 | 2127, 2413, 7257, 206949, 3114613, 5716911 71 | 154, 437, 938, 291386, 595882, 1131382, 677959313, 2626498477 72 | 395, 635, 1615, 52615, 1714535, 4913669, 1248924731 73 | 152, 177, 517, 666, 1345, 4668, 4748, 7576, 12645, 15112, 21324, 67038, 74916, 103234, 148626, 211122, 500834, 1659036, 2933144, 3908664, 4731908, 5617356, 6240072, 21740322, 24805416, 27969852, 35679432, 40371543, 50861652, 51804378, 106044993, 198601181, 584751572, 730392963, 860074374, 1064722712, 1529309961, 6551497341 74 | 1100963, 133436707 75 | 94, 32709749 76 | 303, 4501, 10843, 1234283, 3575901, 147072477 77 | 3082, 7636, 28484, 1278202, 2300069, 11364827, 11834423, 15861628, 167163572, 340166828, 1226293988, 5279926753 78 | 5845645, 14370707, 122199545, 335267879 79 | 730, 1059, 1506, 3090, 3846, 11121, 85481, 3103770, 4766777, 10483566, 24116111, 41341641, 99366863, 124614246, 549940483, 629490830, 795772597, 1600200697, 1977565391 ---+---------------------------------------------------------------------------- 80 | (none under 10^10) 81 | 242, 344, 356, 592, 664, 820, 1160, 1744, 1840, 2096, 2140, 2332, 3088, 5660, 6260, 6940, 14972, 15440, 18392, 22856, 23672, 23836, 27920, 44344, 44368, 64496, 116240, 121334, 181784, 242348, 245680, 447760, 502832, 542020, 599632, 821942, 831836, 978280, 982808, 1150412, 1312460, 1602680, 1770224, 1831736, 2247676, 2658776, 2723320, 2772860, 2838256, 2924360, 3033932, 3152848, 3414260, 3486352, 4342640, 5037988, 5367464, 5850860, 6119749, 7489028, 7816720, 8268280, 8334544, 8990612, 11200424, 12444872, 15792376, 16695880, 16950032, 18345052, 18360740, 21046982, 23097460, 24696892, 25364792, 27682712, 36966152, 38371780, 41612548, 43355860, 43913680, 48043546, 57328720, 57968188, 65641616, 71539280, 74228282, 95619980, 97326262, 98039660, 99828304, 138789218, 178500580, 178971460, 189099760, 196179706, 203588752, 219241352, 257877124, 273054836, 273299536, 276493720, 286275352, 286532432, 298047212, 376964852, 389595940, 466674434, 553666460, 561909392, 654893776, 660637580, 772385036, 775957732, 915967876, 1042338320, 1051782476, 1078700732, 1131172780, 1174211096, 1228075984, 1243235312, 1305169168, 1577531692, 1685185004, 1769932582, 1896235792, 2001256106, 2352824080, 2461526066, 2667659420, 2865894260, 2996695564, 3138105944, 3202094260, 3245813680, 3263229742, 3337375460, 3415593880, 3594910352, 3817249456, 4404424660, 5026512880, 5443514032, 5556790480, 5661063736, 5669274640, 5688889480, 5795507056, 6467510288, 7203982640, 7278317240, 7694057746, 8052099548, 8977766480, 9003511760, 9277619536, 9364938572, 9466720420 82 | 135, 141, 675, 1035, 1695, 2553, 8181, 14499, 14775, 17295, 46575, 53631, 60075, 147575, 186057, 210519, 259443, 1055997, 1152475, 7134555, 8954775, 382547301, 988748975, 3534833097, 5018838675 83 | 86, 7909, 772418, 2660009, 6297269, 31374217, 5207572514, 6581041145 84 | 84557, 333157, 3662559911 85 | 222, 452, 1554, 3962, 3972, 4074, 4438, 7042, 9318, 13386, 13692, 18293, 22494, 32108, 38108, 57702, 155572, 212244, 230132, 902706, 2046156, 4810092, 6369846, 11143868, 14065534, 14542598, 23684514, 30213372, 51013254, 55527906, 65490798, 90049458, 129147074, 313529622, 419156052, 664822497, 974139774, 2587610266, 5959469012 86 | 105803 87 | 235, 1795, 6215, 398594761, 1349662046, 8663162255 88 | 111, 365, 565, 25877, 32205, 111887, 197391, 1152017, 728151231, 9995411859 89 | 110, 424, 1990, 7010, 10319, 11230, 12767, 14236, 40984, 77110, 3768710, 5728910, 6987310, 15391144, 284011606, 286404490, 875048338, 890502472, 1396609310, 4932528472 ---+---------------------------------------------------------------------------- 90 | 679, 646891, 1080871, 36836051, 279758801, 2442967037, 4430530993 91 | 117, 198, 234, 247, 279, 767, 858, 1131, 1209, 2899, 3161, 5174, 8086, 10509, 19401, 21723, 70382, 123762, 633071, 663858, 1739946, 7577011, 13156947, 16454659, 22994127, 46083414, 69624837, 109443077, 201930469, 328591822, 898026282, 1117137538, 2361623147, 3395540997, 4855825806, 5367638601, 7907300167 92 | (none under 10^10) 93 | 145, 2588, 9614, 93746, 217514, 572044, 775316, 6559193, 9850063, 189046484, 2780454314, 8756672293 94 | 1639, 2103, 119597, 52285299, 440603473, 984853293 95 | 1219, 1978, 2881, 134297, 6644999, 133447766, 749551766, 1149758797 96 | 13057337, 614782223 97 | 147, 176, 282, 735, 777, 1056, 1166, 1488, 1855, 2334, 2372, 2455, 2544, 4011, 4272, 4655, 6027, 7998, 11535, 11613, 13578, 14916, 18834, 20856, 21343, 46403, 57144, 168744, 318815, 454728, 476655, 710916, 836616, 871266, 953364, 1251296, 1429296, 1570672, 1724536, 1881915, 1961886, 3179186, 3254736, 3255956, 4807392, 5568366, 5960368, 6213416, 11329592, 27432469, 32553516, 48392476, 82532415, 93502437, 98315772, 195385757, 202305579, 264370656, 501757473, 510437796, 603618576, 633277272, 1110957168, 1838308272, 2157970223, 2851439115, 3631419939, 4693896048, 6723151379 98 | 1985, 7505, 17765, 212245, 6737946073, 8565679313 99 | 350, 490, 518, 1850, 2450, 6286, 7090, 9310, 14098, 36470, 41810, 62230, 98201, 125314, 129010, 129850, 133798, 176890, 240866, 548050, 756518, 956650, 1111090, 1182370, 1939910, 4475170, 5268578, 6013910, 10067602, 13328842, 13844950, 22465030, 74151490, 111694618, 129486406, 205492154, 206304686, 269678570, 384507550, 397122950, 407646350, 759009406, 1480887310, 1589640850, 1785141590, 2166610090, 4533311650, 6781229770 100 | 699, 3277, 486561, 778527, 91009533 ----+---------------------------------------------------------------------------