3^n=c mod n (2 <= n <= 10^10, 1 <= c <= 100) c | n ---+---------------------------------------------------------------------------- 1 | many 2 | 2929, 9742277641 3 | any prime 4 | 41459 5 | 76, 418, 1102, 4687, 7637, 139183, 2543923, 1614895738, 9083990938 6 | 21, 936340943 7 | 295, 883438, 252027511, 7469046275 8 | 2352527, 193841707 9 | many ---+---------------------------------------------------------------------------- 10 | 963400369 11 | 1162, 1692934, 3851999, 274422823 12 | 15, 35, 55, 203, 7467, 11477, 13035, 22715, 148115, 265677, 321755, 4338101, 6699037, 11244715, 18708683, 45840851, 60199189, 63194815, 78873935, 86010731, 184108589, 185952997, 363562103, 398873695, 503736501, 674544929, 796840935, 1260629341, 1549823817, 3191238537, 9239621655, 9896742249 13 | 68, 93034, 1379285, 3114665, 10658684, 185346514, 1049209718 14 | 22082967607 15 | 42, 102, 319, 374, 2814, 5599, 3088806, 24558438, 42105234, 167295209, 439759094, 4481485878, 6573040702 16 | 144937, 919520173 17 | 217, 304, 3272, 240452, 268057, 949837, 2265616, 6067988, 11038393, 16914764, 191871337, 308285608, 1406342497, 2025929395, 2251234858, 3347817007, 3447921938 18 | 25, 45, 171, 207, 225, 1725, 4365, 38925, 130077, 650205, 3241319, 23451111, 342359613, 602890605, 2551762743, 9724070823 19 | 1054, 59030, 64430, 131930, 13512094, 22723390, 42289499, 375798193 ---+---------------------------------------------------------------------------- 20 | 1948397 21 | 60, 204, 354, 1020, 6252, 160476, 995604, 8901426, 67181362, 402097789, 404800602, 1162261460, 1970404118 22 | 14495, 131737, 313157, 20725913, 75007987, 2291078855 23 | 266, 2834645, 3706178, 109769119 24 | 721, 4828159, 65035369, 6076981561 25 | 28, 152, 344, 616, 836, 1918, 2204, 2546, 3572, 3806, 3956, 3976, 9374, 15274, 19432, 76418, 253112, 278366, 303752, 398104, 501886, 885304, 1705816, 1752184, 1884502, 2009116, 2847644, 4262204, 5087846, 6087256, 9188536, 9565948, 16814764, 19162028, 19914812, 33480748, 57685096, 58925624, 92572712, 93853564, 125295494, 175850836, 246794296, 391352219, 478559416, 488661422, 492630376, 559427176, 641270363, 730992404, 799859048, 859050346, 1147759646, 2716415036, 2742918376, 3229791476, 3322784516, 4848295496, 4997034044, 6360767783, 6761890792, 7795187546 26 | 4343 27 | many 28 | 193511, 15210347, 169859609, 194249963 29 | 52, 130, 2270, 25517, 46891, 4643183, 11301977, 13289770, 344804270, 587516246 ---+---------------------------------------------------------------------------- 30 | 6884974839 31 | 49, 108409, 937117, 1329239, 19832197, 1873560058 32 | 1055, 91775, 9843355, 30848275, 352124735, 431236775, 577271735, 581797075, 6749428295 33 | 48, 96, 136, 174, 408, 592, 744, 1245, 2513, 7918, 41136, 66774, 132852, 193904, 1086672, 3917216, 3940584, 12641064, 17119272, 18962344, 53900304, 248869365, 398514498, 1140353608, 1830636816, 1906442192, 1993842118 34 | 622699582951 35 | 39806, 393926, 4721111, 30500362, 97012759, 195070811, 227346314, 3109337753, 4509734017, 9040411214 36 | 333, 531, 501561, 1594521 37 | 44, 515, 979, 2189, 63121, 193276, 402548, 2417996, 1391116622, 6754552739 38 | 205, 2149, 7421, 26057, 3142445, 10273333, 971342029, 1344626311, 4998530713 39 | 70, 138, 2810, 117570, 374190, 2232034, 2675982, 4212030, 5004478, 174081594, 503620053, 3228235610, 8869003446 ---+---------------------------------------------------------------------------- 40 | 791, 39121, 263279, 60579397, 5196535819 41 | 460, 1180, 1304, 11320, 31429, 54116, 1173421, 1284740, 1814671, 2033960, 4620689, 67698262, 120283172, 451162198, 6668432780 42 | 335, 129877, 140491, 305295, 531427, 885697, 3263555, 5043415, 138420061, 182727113, 641592915, 2709426715 43 | 725, 5825, 13414, 40925, 2148862, 70832914, 128535518, 184664126, 1112387002 44 | 439889, 18346721, 245061961 45 | 114, 348, 1962, 6108, 9819, 23542, 83172, 110853, 228996, 1129131, 1777158, 2223114, 2301239, 2755098, 3727428, 4750509, 15887484, 35294418, 48043311, 53467164, 70000207, 79306478, 192268068, 364895301, 597015999, 725413173, 1016825482, 1544411844, 2900128861, 7238083851 46 | 247275757, 2773135357 47 | 506, 749, 401606, 2780839, 15206315, 35058635, 78053759, 100727066, 1432992506, 2518236346, 3237322846, 3430181615, 5630668597, 6677056234 48 | 65, 105, 147, 209, 377, 885, 1785, 2629, 2813, 3885, 5061, 5709, 7685, 10441, 13209, 14573, 17871, 18105, 18377, 23961, 37113, 42105, 49053, 59829, 78845, 85957, 86687, 108465, 109997, 113505, 121393, 159045, 216579, 263549, 354165, 541317, 657705, 814821, 946985, 969623, 1240113, 1813665, 2491705, 2491977, 3653233, 3970265, 6101385, 9598785, 11036865, 12343019, 13188605, 16260945, 19394285, 22020159, 22586989, 23144601, 24836669, 26093865, 30473881, 32089953, 40242585, 41448787, 44779241, 52595571, 55465085, 59592287, 100662185, 104052665, 105424905, 125798505, 143633321, 144901785, 191203401, 195890505, 230561281, 234433689, 248525193, 261845481, 275545673, 278904685, 310288209, 311301965, 331788945, 389882145, 426265185, 450185799, 507816005, 520729145, 546658513, 559777985, 644849139, 1012013823, 1165108677, 1215952601, 1362748799, 1365029589, 1393824369, 1483732005, 1534559145, 1649349665, 1816596217, 1840627785, 1882934445, 2034360005, 2207720793, 2496430293, 2872010199, 3249049587, 3500971421, 3527784145, 3773471113, 4244245761, 5438571873, 5747788253, 5795135489, 6979561149, 7102213383, 7553660745, 8120312781, 9357479337, 9851938089 49 | 50, 88, 296, 464, 590, 803, 1628, 1808, 5336, 9328, 13136, 13343, 25070, 35450, 51026, 52432, 68918, 91408, 230689, 262310, 278168, 1766876, 2706050, 3674747, 5839052, 7400228, 11419178, 14060924, 15655450, 16189118, 19430150, 20227988, 20246872, 37651108, 37940156, 81595286, 83111816, 118945072, 129322450, 170265512, 214696670, 234576152, 273051670, 278497616, 307744816, 311465968, 362907352, 373862588, 418305488, 504055022, 600934598, 680312432, 779074256, 907859528, 978068456, 1487895068, 2041943216, 2264211850, 4021166399, 4279970288, 4290309272, 6426609010, 9161245367 ---+---------------------------------------------------------------------------- 50 | 764353, 224072473 51 | 678, 6062, 193894, 210946, 988842, 3656986, 48055031, 254054811, 920123621 52 | 427, 955, 9441397, 16948057 53 | 238, 1121, 26614, 107767, 276431, 457945, 653012, 974017, 1420759, 3596252, 5292341, 6279892, 6535988, 18300266, 48001505, 1054626583, 7971889396, 8545035596 54 | 837, 6543, 58167, 180333, 683281, 12447957, 36829917, 338508747 55 | 403, 559, 3683, 52702, 146903, 785074, 5432206, 9930526706 56 | 50369033879 57 | 75, 84, 155, 168, 255, 375, 1218, 2168, 2982, 3875, 9618, 27678, 28434, 37956, 140375, 273575, 350232, 1062471, 1237928, 2764824, 5794508, 12020442, 57891036, 63066468, 65018478, 133777308, 137932276, 195927672, 425666877, 508233642, 1425260075, 4340747615 58 | 185, 851, 524842411, 3678595259 59 | 133, 170, 3470, 938581, 1433014, 2449669, 3142970, 8962243, 20616073, 32543374, 49087910, 341616994, 593833769, 797826799, 1203709691, 1975344010 ---+---------------------------------------------------------------------------- 60 | 16999, 301983, 451803, 6222641403 61 | 260, 9737, 31577, 9806938, 16583684, 19385249, 20631860, 42056963, 56007268, 2474049938, 5143539020 62 | 391, 4471 63 | 222, 765, 981, 3165, 30858, 31958, 48726, 143118, 188445, 785494, 5229654, 5729546, 15557679, 77551974, 120098961 64 | 1829903, 125638117, 2812093549 65 | 224, 232, 1856, 3122, 5728, 294176, 332864, 352448, 1030496, 2508563, 2690416, 5042981, 22961632, 32168207, 38871694, 71110976, 115762336, 170932328 66 | 4251, 161893, 265614497, 7648605861 67 | 54048442, 247615606 68 | 125, 245, 325, 6125, 211799, 863419, 2972125, 3784025, 4181125, 11314373, 13325779, 24641125, 81401125, 154469125 69 | 231, 5730, 7453, 8310, 9830, 17116, 40858, 83391, 91599, 235239, 531372, 570092, 13207299, 27588369, 38237343, 136662141, 238206182, 244422790, 363289101, 475470597, 811308201, 1945783470, 8490066190 ---+---------------------------------------------------------------------------- 70 | 84689, 4137859, 479289019 71 | 43646, 193486, 283757, 2572337 72 | 95, 1035, 19611, 570749, 1466429, 7324367, 30073387, 55401771, 76642177, 80836949, 117759381, 366077951, 2600373821, 7475985063 73 | 85, 1057, 1558, 6488, 1267642, 6369593, 184434974, 4707093656 74 | (none under 10^10) 75 | 77, 187, 654, 1562, 3597, 3979, 4399, 4991, 16037, 18011, 94299, 94319, 290139, 626359, 1919069, 1958091, 16567431, 16865607, 26828051, 30451011, 45586641, 200018357, 311612429, 363868482, 842396849, 1334245117, 3515713611, 4157667987, 6112580119 76 | 6751, 22849, 28981 77 | 415, 989, 23338468, 31424194, 59827868, 192219004 78 | 165, 297961, 1792465, 447381843, 1980305305, 2350610445, 4790734765 79 | 98, 602, 4214, 45710, 47390, 58970, 62006, 195082, 209141, 910906, 1261190, 3009277, 28802690, 43046990, 362316710, 393253490, 1517181529, 4525283966, 6443876287 ---+---------------------------------------------------------------------------- 80 | 301, 2107, 5047, 4009621, 6790861, 7752241, 29544109, 30376909, 1859891341, 1992257827 81 | many 82 | 115, 5034155, 25873475, 119567575, 243305651, 961110935 83 | 269233, 325213711, 716280871, 2367302402 84 | 15789, 39387, 285627, 11474157, 24343089, 426993261 85 | 493631, 1287668, 1953209, 404861818 86 | 9021827, 672857441, 5179111813 87 | 642, 7046, 8094, 199255, 607327, 4480053, 10670738, 88234969, 135389191, 393185658, 1601715261, 2437345007, 2866082935 88 | 114694213 89 | 110, 670, 6472, 7343, 23596, 46493, 3684664, 113482198, 353043388, 1726232782, 9073066229 ---+---------------------------------------------------------------------------- 90 | 357, 2799, 5555309, 19540437, 205104963, 645280557, 791179977, 1102923171, 1548732969, 7465069143 91 | 342034874, 948028741, 2397446546, 5260799554 92 | 755, 112164817 93 | 253, 308, 318, 1358, 1518, 2618, 14113, 531348, 699925, 2449308, 5043925, 5699078, 6025124, 7232348, 22551284, 31208362, 110577698, 133518308, 177722925, 183804258, 381168196, 1576494462, 4931239372 94 | 6097, 4363861 95 | 136867, 27177889, 33480118, 42918943, 81790622 96 | 119, 287, 13258111, 14895841, 43971311, 120334199, 1055730021, 4329735809, 4386041761 97 | 352, 808, 15181, 31396, 39952, 69569, 1822112, 2470072, 10898708, 21523312, 87076517, 87245728, 212313688, 2454434452, 2958437344 98 | 145, 1728605765 99 | 126, 150, 153, 210, 294, 450, 630, 882, 950, 1050, 1310, 1470, 3150, 4410, 7146, 7350, 11046, 18050, 19782, 22050, 27882, 34050, 35850, 137550, 217266, 297318, 518910, 705558, 725130, 1038090, 1626450, 1668047, 1954650, 2651450, 5799150, 19501434, 38448441, 50733230, 56667570, 57863610, 110998818, 146150046, 157219146, 193175430, 196325174, 362109510, 409664850, 478984710, 601922150, 739138050, 1079004150, 1865018201, 5150345130, 5964487946, 6611216850 100 | 4058603, 20724899 ----+---------------------------------------------------------------------------