2^n=c mod n (2 <= n <= 10^10, 1 <= c <= 100) c | n ---+---------------------------------------------------------------------------- 1 | no solution 2 | any prime 3 | 4700063497 4 | many 5 | 19147 6 | 10669, 6611474 7 | 25, 1727, 3830879, 33554425 8 | many 9 | 2228071, 16888457, 352978207, 1737848873 ---+---------------------------------------------------------------------------- 10 | 18, 16666, 262134, 4048124214 11 | 262279, 143823239, 382114303, 1223853491 12 | 3763, 125714, 167716, 1803962, 2895548, 4031785, 36226466 13 | 95, 4834519, 156203641 14 | 1010, 61610, 469730, 2037190, 3820821, 9227438, 21728810, 24372562 15 | 481, 44669, 1237231339, 1546675117 16 | many 17 | 45, 99, 53559, 1143357, 2027985, 36806085, 1773607905, 3314574181 18 | 35, 77, 98, 686, 1715, 5957, 18995, 26075, 43921, 49901, 52334, 86555, | 102475, 221995, 250355, 1228283, 1493597, 4260059, 6469715, 10538675, | 15374219, 19617187, 22731275, 53391779, 60432239, 68597795, 85672139, | 175791077, 271249463, 347558057, 668863235, 870842275, 981624497, | 1018784797, 1110648455, 1184179153, 1523318435, 1830772675, 3896018897, | 4269036653, 4589247047, 5117126315, 7800075437, 9199245587 19 | 2873, 10081, 3345113, 420048673, 449349533, 2961432773 ---+---------------------------------------------------------------------------- 20 | 2951, 926753239, 960640071, 1367105963 21 | 3175999, 54895651 22 | 42, 13746, 1048434, 319754822, 350849483, 3808053518 23 | 555, 80481, 41546509, 967319517, 2196415073, 5094927987 24 | 50, 232, 81028, 35622023, 125531078, 161524561 25 | 95921, 24960497, 3594750257 26 | 27, 2714, 17861, 24099, 336326, 364634, 26153222, 67108851, 67716217, 249689933, | 3635254431, 5149603863 27 | 174934013 28 | 36, 54, 108, 1356, 2041, 14562, 24084, 38286, 48492, 3494412, 4473836, 4689061, | 120851622, 747463758, 846188887, 974629932, 1259182969, 2317452156, 3490949934, | 3785858532 29 | 777, 56679, 274197, 2359749, 2804637, 4657821, 5212515021 ---+---------------------------------------------------------------------------- 30 | 49, 238, 57526, 73843, 143702, 876169, 6588043, 7930534, 12971534, 14561758, | 40669406, 148300193, 7980170978 31 | 140039, 404167811, 1767944407 32 | many 33 | 2463240427 34 | 110, 330, 1410, 3210, 9570, 19410, 126390, 150281, 299454, 4743530, 4980413, | 9155410, 9767670, 18652278, 19288886, 19731394, 74425294, 149839810, 200302062 | 2709330690, 3426561062, 9802150230 35 | 477, 671, 41817, 111771, 683147, 893541, 901077, 3261731, 29265401, 175933791, | 1161951851 36 | 697, 1738, 2060, 10180, 21338, 500089, 552838, 9142057, 13222948, 25883182, | 85338940, 155386292, 328137220, 425288468, 575986804, 937311724, 4229524340, | 4938510140, 5478903118, 8285486788 37 | 91, 14364571, 61924805, 1222572623 38 | 578, 5882, 86407, 7098418, 28702677, 101511658, 241304631, 1692548594, 2423605022 39 | 623, 62771, 8176423, 1054773269 ---+---------------------------------------------------------------------------- 40 | 156, 312, 16692, 99996, 1290552, 3319212, 4754856, 8719464, 18537061, | 51767236, 101017176, 591107761, 1737492721 41 | 2453, 35457, 584349, 57084101 42 | 540923, 86133422 43 | 55, 275, 935, 7871, 31597775, 4667597275 44 | 70, 117, 1204, 3010, 34281, 57993, 113890, 275716, 2556716, 4667908, 4731757, | 37015930, 63138964, 65606901, 91496318, 400517013, 1937428486, 2176322019, 4308937893 45 | 345119 46 | 287, 38586, 202842, 262098, 476567, 796523, 1417361, 15775487, 28789163, 249572574, | 1501259186, 6026576646 47 | 1131, 12585, 143321, 21086871, 24741253, 115078479, 248556333, 994200485, 7396887959 48 | 104, 572, 4324, 8684, 8878, 12428, 65488, 524282, 1322672, 16062332, 32680792, | 46612996, 50107112, 50231908, 134853496, 356698651 49 | 943, 1075439 ---+---------------------------------------------------------------------------- 50 | 147, 1311, 4047, 4389, 7791, 21399, 1643561, 1989403, 2543203, 3233171, | 3630849, 5858261, 16297953, 17009517, 17206359, 17630529, 31678719, 80455431, | 165915267, 315494863, 409009713, 477499323, 586788573, 2482230093, 2993882163, | 3010350957, 4188910071, 6925297449, 9805515121, 9964180149 51 | 21967 52 | 4044, 46506, 112636, 255012, 7863277, 8119513, 26362177, 279393612 53 | 135, 153, 15255, 17557, 32249, 167355, 298215, 664031, 2688835, 5293215, | 5368707, 40661609, 71224787, 392617395, 836687595, 2086615593 54 | 970, 4069, 14782, 108058, 2089874, 3531133, 3871642, 11486074, 39563002, | 69263626, 89163370, 164535110, 165674821, 253223990, 272757277, 650983367, | 862876213, 918530362, 1078365647, 1106641861, 1154529370, 1591305554 | 2685182638, 3354132010, 4381581982, 5826750829, 8441351806 55 | 46979 56 | 220, 440, 1742, 47660, 49060, 250406, 570680, 1478840, 42843656, 204288440 57 | 125, 925, 1991, 2378239, 128115025 58 | 59378, 169978, 2508978, 3858733, 18656197, 59838019, 971506018 59 | 3811, 10279, 35243, 236919, 549677, 11633491, 17572963, 193069749, 273813811 ---+---------------------------------------------------------------------------- 60 | 119, 841, 25546, 30001, 79543, 109508, 480452, 5586631652 61 | 23329, 62689 62 | 345, 598, 1185, 101545, 129922, 196534, 4643722, 6403765, 11748297, 75872987, | 359750385, 505257766, 2046554283, 2512161605, 4471885238, 5878680026, 6876977385 63 | 155, 9607, 1018303, 8234588153 64 | many 65 | 1064959, 1112340129 66 | 3007, 189247, 804779, 1388014, 11832917, 6804148493 67 | 245, 665, 22505, 4312637, 4931279, 17002765, 26068931, 44322787, 100893853, | 150322861, 359764979, 795934871 68 | 75, 375, 1635, 4521, 5575, 12975, 23764, 40875, 100875, 313475, 655611, | 4902711, 17706075, 22505775, 25304042, 1939304967 69 | (none under 10^10) ---+---------------------------------------------------------------------------- 70 | 1990362, 17993382, 33478901, 44328514, 378654109, 2308380602, 2647901363 71 | 19719, 699027, 2223121, 4304727, 36336687, 98719037, 690212817 72 | 184, 209, 2485, 28546, 69361, 70861, 129485, 679714, 716753, 1512151, 1612021, | 69956503, 107224651, 122681965, 227506133, 280727965, 574282505, 613566754 | 6771374489, 9042928583 73 | 834976783 74 | 190, 350, 1353, 37150, 151550, 379810, 525333, 1332590, 46970067, 71864043, | 682530487, 831884921, 1009373602, 2644584950, 2698486490 75 | 4029547, 13547021, 1200557377 76 | 100, 300, 804, 1369, 4379, 4660, 74908, 75100, 136700, 145380, 182100, 3032300, | 87139068, 505917044, 792909683, 3090091300, 6143110531, 8010530700 77 | 1207, 80480417, 102282447 78 | 115, 70682, 69107959, 166155082, 287044817, 307407998, 312176815, 676861873, | 6525513494, 9639960074 79 | 931, 4081, 8113, 140371, 153301, 243281, 1855913, 808742011, 8168972581 ---+---------------------------------------------------------------------------- 80 | 81, 88, 169, 999, 8397, 65456, 919162, 5767058, 89080178, 171259467, | 2228267992, 3123612578 81 | 329, 27562303 82 | 162, 414, 594, 2438, 3618, 3798, 178902, 189342, 291461, 2579021, 11124378, | 15378814, 51136002, 113912914, 523414566, 819763038, 3361082238, 6460590078 83 | 429, 76089, 7684989, 55133013, 66602913, 68556189, 193336869, 263920053, | 384902197, 1076243493, 2084914689, 3451125441, 6831559293 84 | 470, 56330, 10785230, 42368236, 327003076, 718164116, 1701333412 85 | 143, 3308903 86 | 406, 3934, 27202, 40399, 5890089, 14821582, 17989977, 395292562, 1922033342, | 2142623182 87 | 18607, 71665, 94001 88 | 812, 1358, 1652, 2004, 4498, 8376, 48072, 60034, 513166, 719432, 8386489, | 17924648, 18887624, 33469572, 124071815, 1930937494, 2721328188, 5295198354, | 8983977778 89 | 423, 317551, 1185243, 12427689, 17392959, 227234169, 322020891 ---+---------------------------------------------------------------------------- 90 | 6631, 18601, 39121, 429602, 228693421, 2851816231 91 | 5422229 92 | 105, 104853, 933747, 2282734, 4674532, 13897745, 22874565, 83314689, | 96289577, 176534185, 3286951737 93 | 175, 595, 3115, 3859, 402019, 10833283, 246862241, 1038678277, 1176882815 94 | 310, 930, 229090, 8973478, 34636830, 1824164178, 9457469989 95 | 4991, 197941, 4044459, 26029239, 100413687, 244820827 96 | 160, 5536, 6544, 13708, 26291, 49520, 127774, 131060, 187360, 209761, 993056, | 9311711, 45908920, 105508072, 920505632, 930305260, 2453441740 97 | 2076287, 21094385 98 | 207, 495, 923, 1537, 14495, 29535, 67535, 103179, 161523, 203395, 7268495, | 19776819, 21470735, 42213435, 65429781, 285657695, 403210155, 659128415, | 758548855, 1337652195, 1422189801, 1464335015, 1543346289, 1740154419, | 4477031535, 5629636791, 7579239415, 8181606189, 9084106481, 9542674135, 9866735815 99 | 202201409 100 | 322, 444, 522, 826, 828, 1334, 1476, 4518, 5004, 11454, 24254, 32788, 33332, | 119498, 520996, 524268, 1348428, 4796596, 6091268, 10392044, 15968466, | 32234486, 40058476, 57371772, 69346674, 160232052, 213381332, 225461036, | 247287046, 251382402, 305728146, 380953988, 398169372, 1155476522, | 1621958196, 1852061812, 2281369668, 2592790892, 2806360218, 3131892084, | 5274648196, 6901744772, 8096248428, 8227973178, 8275461156, 8364843068 ----+----------------------------------------------------------------------------