19^n=c mod n (2 <= n <= 10^10, 1 <= c <= 100) c | n ---+---------------------------------------------------------------------------- 1 | many 2 | 17 3 | 358, 14266922, 239658166, 782137769, 1200856619 4 | 5, 15, 1371, 1915, 2155, 3345, 22395, 4441069, 14087235, 4591919091, 6973717969 5 | 7, 178, 4582, 88963, 130316, 313283, 2522903, 3434473, 10817863, 85357004, 826230836, 1775147398, 2954363158 6 | 13, 949, 50629, 2543743, 138254009 7 | 118, 318, 1713, 2022, 2634, 26611, 93489, 42326429, 476402478 8 | 11, 1142723, 479672759, 533155187 9 | 22, 28, 52, 184, 242, 248, 364, 716, 3514, 6292, 8408, 17524, 22664, 39058, 40612, 49622, 68002, 75578, 182572, 209404, 375982, 470932, 512762, 677962, 680494, 781114, 997208, 1199848, 1238045, 2492632, 2682568, 3069254, 3566648, 4455724, 7080232, 9352328, 9584186, 10756732, 13597012, 15068372, 16561658, 22623172, 28533844, 85325812, 96889514, 122246542, 145764728, 158707654, 220689196, 251952458, 259867192, 375247862, 479316332, 568985032, 663629032, 761012036, 911248022, 928859215, 1006770637, 1059813832, 1564275538, 1818350716, 2110364264, 2401713238, 2800866662, 3434740348, 4051461224, 4231156072, 4473726536, 5431066984, 6319400692 ---+---------------------------------------------------------------------------- 10 | 207, 2283, 52729, 172089, 733743, 3812411, 5798009, 1402531529 11 | 14, 530, 135170, 5989573, 37167242, 39305347, 146230490, 4229653022 12 | 6683, 8323, 93221473, 1750335089, 9168026287 13 | 21, 58, 102, 489, 618, 2148, 11028, 13434, 43436, 3657137, 4465668, 6684387, 24186286, 325182183, 739098759, 957147807, 1091018289, 1613074524 14 | 1055, 7015, 11735, 12505, 10516705, 63709315, 442118785, 1251904145, 1958207665, 2641364965, 2904390865 15 | 221, 346, 533, 13354, 1340174, 2201858, 3869074, 521378647 16 | 6843, 135466869 17 | 86, 2036, 3941, 25192, 31792, 47302, 50981, 99928, 321554, 361582, 451586, 679832, 4749653, 140258264, 1271434694, 4105708004, 5658013613 18 | 39959, 1076567, 20643929, 2993730137 19 | any prime ---+---------------------------------------------------------------------------- 20 | 559, 477168647 21 | 34, 170, 5212, 10547, 61790, 9282170, 16062380, 42333580, 166116389, 419628470, 689455706, 1675752422 22 | 129, 159, 89421, 2280923, 14068869, 2168980347 23 | 26, 338, 96434, 253126, 19519838, 102552242, 1477942691 24 | 25, 35, 77, 455, 707, 4511, 30443, 70745, 259175, 2333807, 2455895, 6372275, 299118175, 688307299, 1505360675 25 | 51, 56, 66, 78, 138, 201, 232, 244, 356, 644, 856, 894, 2668, 9164, 10956, 12714, 16946, 22402, 22946, 43736, 54186, 60294, 62904, 120846, 163194, 177926, 260632, 386744, 391956, 614884, 626566, 807052, 2150088, 3649206, 5045806, 5462556, 5922456, 6352404, 6717326, 6868946, 8126502, 11190314, 11914436, 17014836, 17260386, 17752424, 19156486, 20532264, 21635726, 27994652, 35524664, 36703848, 37497268, 42785886, 80211736, 94091772, 100717464, 131377026, 141137628, 163151736, 170714008, 177005864, 177746316, 215525114, 226674564, 274912152, 296066876, 562184916, 743888676, 748296626, 793091188, 891425292, 897289971, 1358466253, 1652461672, 2262197796, 2501509346, 2653308098, 3550294796, 4541388362, 5076878936, 5788990632, 5908726316, 6759021701, 7045566888, 8641983246, 9126674574, 9283849923 26 | 799, 2443, 150661 27 | 334, 542498, 3099544913 28 | 33, 69, 1587, 10467, 40157, 107379, 1223577, 6549649, 6774903, 8126343, 28808741, 53547397, 79280223, 92487159, 191852091, 499088859, 504194661, 1841557401, 7879152819 29 | 166, 130292, 1238035, 5370914, 62351588, 643207169, 1577182762, 2472129092, 7095380548 ---+---------------------------------------------------------------------------- 30 | 47427581, 5106239387, 6195865289 31 | 1537, 1707, 23830, 46293, 874013, 1881834, 2343846, 52648883, 261538546, 521425163, 857611730, 1523371098, 4268503830, 7464147014 32 | 901, 51493, 65501, 9241013 33 | 68, 82, 91, 592, 1328, 1916, 3679, 22376, 73481, 182036, 189752, 205508, 8929441, 19985312, 88168732, 106124551, 411071011, 644208382, 5526893827, 6811152808 34 | 39, 105, 115, 195, 12345, 28119, 35885, 102687, 121595, 204729, 504231, 1022235, 1419595, 2071435, 12034223, 35842755, 66339755, 78351195, 9326751041 35 | 326, 3293, 4922, 656386, 1272571, 10717838 36 | 87169, 130441 37 | 44, 154, 188, 1137, 1474, 2796, 3636, 28204, 44532, 88522, 104772, 113231, 153274, 255574, 360389, 1203322, 1688826, 3791452, 3810554, 4054204, 7840974, 107901938, 232940554, 243216522, 362661996, 710247292, 960788183, 1024880458 38 | 161, 324653, 359309, 1918207, 8093729, 11486647, 155139761, 362474273, 490349927, 5667405097 39 | 46, 58333, 505499, 619015, 3107765, 136075165, 198061853 ---+---------------------------------------------------------------------------- 40 | 3509, 6819, 21763, 5551593, 2270289381 41 | 341, 472, 1130, 7316, 13028, 14996, 27401, 51857, 659240, 879878, 2302856, 38952040, 259044580, 728770540, 2206418360, 3391076470, 6836109206 42 | 529, 12167, 1040737, 148396667 43 | 106, 213, 1758, 11298, 22938, 116194, 131082, 159954, 232679, 291259, 49919343 44 | 1098179, 2476055, 271210309, 9265350917 45 | 158, 16678, 29698, 130276, 794158, 1988278, 2461636, 6238378, 17508118, 67157279, 482158261, 523590301, 3128550929 46 | 657, 2271, 8217, 196191, 202779, 1471507, 3706331, 6749361, 7876873623 47 | 314, 506, 8091446, 7914946979 48 | 49621349, 167830633, 7576312369 49 | 75, 85, 88, 92, 236, 296, 348, 528, 636, 681, 1095, 1104, 1628, 1808, 3058, 3088, 3426, 4044, 4696, 4855, 5268, 6064, 11848, 17616, 19668, 20598, 22418, 26332, 38856, 53222, 76044, 77968, 117276, 161124, 186978, 361846, 464368, 623972, 712317, 753072, 1066189, 1196225, 4001104, 4513074, 5468626, 7012176, 9619368, 9661936, 12263984, 13843598, 15661228, 17197072, 19254525, 20564592, 21498074, 29659058, 44957334, 65973342, 80606832, 81758762, 84652858, 123284085, 218407422, 221199952, 225210984, 235427568, 260698632, 279799388, 289090212, 346042975, 357939332, 400792048, 512723895, 548430856, 625807986, 733490544, 952804956, 977868942, 1103010712, 1397125928, 1418800184, 1635801144, 1695900118, 2018966268, 2501617542, 2644461908, 3281045776, 3305943044, 3754977186, 4858336464, 4885491248, 5065609085, 6928397925, 7073642342, 8854125122 ---+---------------------------------------------------------------------------- 50 | 143, 583, 3688723 51 | 62, 70, 470, 590, 4210, 9478, 11450, 24430, 27350, 29350, 30010, 85582, 283150, 1378210, 5806982, 6572950, 834799510, 1306221947, 1651438969 52 | 749, 6807, 120597, 230397, 493691, 1387957, 2168327, 2433973, 4817791, 19492529, 37814189, 46408901, 64234283, 152106573, 552860121, 6991256289 53 | 116, 4492, 8204, 93044, 96362, 353402, 3108151, 3434876, 11387332, 31924468, 34414273, 2805355364 54 | 55, 65, 385, 2405, 4015, 17315, 372295, 501655, 3063905, 3876985, 6125455, 27714005, 89880385, 391900919, 6364775285 55 | 63, 189, 306, 783, 1266, 2407, 4431, 9342, 19593, 24774, 97794, 163269, 279951, 615573, 3319533, 8627382, 23210179, 30493854, 50592297, 961950339, 1060274277, 1352114586, 1372206006, 1676780694, 3011419197, 3841520211 56 | 1943, 7492643 57 | 76, 152, 407, 2014, 3428, 20444, 28234, 33142, 48184, 90497, 196424, 645202, 1266578, 1514804, 1917352, 2100317, 5273974, 85587716, 115573162, 274683733, 893871736, 1271894003 58 | 2509, 6801, 2422322773, 7548643021, 9522364359 59 | 185, 302, 1195, 135187, 177395, 298445, 333077, 679505, 1362574, 5582866, 32114407, 44607815, 146811562, 149274334, 726706774 ---+---------------------------------------------------------------------------- 60 | 291284783, 1840815281 61 | 259, 309, 668, 1679, 4780, 7073, 51540, 92749, 163426, 176332, 1051370, 4116351, 4704582, 6336420, 7243820, 9719170, 12401179, 365612070, 421593213, 1198849110, 1578529860, 2025224430, 3104104223, 7218239540 62 | (none under 10^10) 63 | 298, 5759, 117970553, 134547047, 234918506, 1068105322 64 | 453, 4113, 5745, 6231, 6465, 10035, 47263, 67185, 91705, 470895, 13323207, 42261705, 51747765, 56105421, 141219999, 149473407, 967516343, 976503705, 4198913847, 4881982377, 7821889113 65 | 74, 112, 448, 1918, 4652, 11456, 19384, 96704, 755104, 868306, 1039637, 1752328, 4822216, 6893648, 12422638, 24125917, 67194808, 162105832, 215376574, 633285568, 1349656042, 3542184374 66 | 1037, 22117, 138551, 316127, 7087477, 1264186997 67 | 98, 849, 2869591, 2907042, 47045814, 291419098, 1557290071, 3556189066 68 | 12397, 44297, 92617, 5364961, 11608723, 59783647, 601512967, 2810992849 69 | 146, 286, 1147, 1826, 20212, 25246, 130252, 156545, 174365, 1238015, 5055742, 5965238, 40957796, 53088374, 376437235, 394945601, 4053741365 ---+---------------------------------------------------------------------------- 70 | 93, 219, 2193, 20553, 370617, 8353137, 8916609, 17558319, 35260329, 1449264297 71 | 730, 3551, 6070, 23033, 82070, 802990, 810434, 1546642, 3811330, 4325774, 40770518, 138364430 72 | 473, 2124461, 1839068803 73 | 87, 99, 268, 276, 666, 7464, 18342, 127944, 190203, 270387, 1503099, 1960242, 2964366, 3061602, 10931231, 14645916, 21309209, 40253684, 73355202, 230774308, 377834597, 894335044, 940775979, 1887062552, 3450363468, 8409099852 74 | 575, 46231, 495205, 14585413, 7624115825 75 | 154778, 7660874, 17756878, 55866979 76 | 299, 323, 399, 1311, 1407, 1533, 2679, 2829, 4161, 7163, 10523, 13091, 14673, 15283, 25009, 113253, 123753, 245051, 275633, 276431, 369453, 424441, 442187, 861897, 1468259, 1667627, 1951509, 2769963, 5221207, 5299581, 6964629, 7462947, 10392087, 11500211, 12440589, 24788711, 26413439, 26561639, 26589003, 27577389, 40699919, 40870771, 43614543, 58080999, 69356289, 73355867, 86636181, 87753107, 123645297, 124672989, 141346453, 155476883, 162400999, 184053513, 363451867, 701758533, 765961041, 894494939, 945324669, 1036465143, 1081930737, 1779002547, 1878519227, 2101939581, 2799640263, 3410569029, 5187514773, 5392347429, 5824243163, 6866281259, 7258968373, 7701695489, 7894643243, 8774783031 77 | 142, 130244, 1156817, 9111196, 301241782, 1986034178, 3832932652 78 | (none under 10^10) 79 | 94, 145, 339, 957, 2595, 4395, 7115, 9255, 18345, 40217, 44805, 107985, 212858, 360595, 547437, 1922538, 2726626, 4032865, 13624654, 17799997, 20406315, 47045802, 66563854, 99224445, 118026422, 120732585, 420928522, 526244718, 598933526, 612635422, 1086108015, 2150038041, 2655111634, 2918557545, 3127739297 ---+---------------------------------------------------------------------------- 80 | 371, 1127, 1291607, 1447271, 52866749, 183737551, 1503071297, 4530709001, 4991819417 81 | 104, 140, 148, 260, 368, 374, 484, 496, 560, 728, 820, 1040, 1190, 1432, 1480, 1508, 1694, 1720, 1820, 1946, 2320, 2980, 3206, 3910, 4004, 6440, 7028, 7280, 11374, 12584, 16520, 16816, 26680, 35048, 45328, 55640, 58756, 65156, 78116, 81224, 99244, 104264, 110540, 121016, 136004, 141596, 147056, 151156, 175096, 183964, 238160, 355540, 365144, 387964, 414440, 418808, 563024, 638924, 704720, 710932, 730696, 751310, 751964, 941864, 985040, 1025524, 1203020, 1319384, 1355924, 1360988, 1393996, 1494740, 1552270, 1561360, 1562228, 1928108, 1968176, 1994416, 1994564, 2099380, 2226856, 2399696, 2476090, 4256840, 4413710, 4570820, 4985264, 5247632, 5272280, 5365136, 5433580, 5929268, 6138508, 6190270, 7133296, 8555074, 8810480, 8830280, 8911448, 8949404, 11378020, 11713520, 12103024, 12909260, 13273520, 13803940, 14160464, 15774920, 16022960, 16220204, 16755574, 17402416, 18704656, 18729352, 19168372, 21513464, 23184140, 24761020, 27194024, 29036782, 30136744, 33123316, 34058990, 45246344, 45996880, 48595984, 51998660, 55857020, 57067688, 57275504, 67040476, 67805380, 67889260, 69184120, 79839410, 84533960, 87614540, 88340720, 115714276, 116539220, 125048948, 141121180, 154401860, 163210780, 169990964, 170651624, 184025176, 193779028, 204847544, 211352540, 213485240, 217447580, 233360120, 244493084, 262123660, 291529456, 293770568, 317415308, 319735472, 326419340, 361355140, 372085274, 382240780, 441378392, 473431880, 500279990, 503904916, 519734384, 584464334, 627994640, 635948540, 649776220, 652924280, 657935920, 670996508, 702427280, 702999940, 750495724, 803633620, 958632664, 1027315784, 1098720328, 1114406744, 1137970064, 1143539248, 1161676040, 1183831522, 1194947420, 1209818984, 1246593296, 1327258064, 1426111132, 1483070740, 1522024072, 1635230012, 1670370340, 1822496044, 1857718430, 1912040036, 1979149684, 2013541274, 2050065974, 2119627664, 2149146796, 2352610340, 2577228880, 2595010540, 2652749840, 2655426956, 2662898420, 2871026606, 3128551076, 3436458116, 3563770352, 3636701432, 3663275380, 3721299824, 3961161620, 4220728528, 4367717480, 4574552764, 4602754480, 4666946110, 4803426476, 5434740176, 5601733324, 5674035224, 5691913168, 6832619356, 6869480696, 7330413520, 7421403080, 7471795856, 8102922448, 8462312144, 8486930480, 8947453072, 9573926180, 9746306960 82 | 753, 49977, 78443, 162207, 268953, 1984491, 16778511, 25417113, 25687333, 275064307, 927986247, 1035042867, 2532746991 83 | 278, 223523, 505189, 10253246, 110331659, 592954373, 1783347313, 3190868557, 7634608258 84 | 505, 649, 9715, 24515, 1085423, 3326215, 72614455, 2741346289, 8645383459 85 | 222, 1554, 3387, 43412, 50509, 53682, 55524, 90822, 131443, 293988, 344126, 523698, 3824394, 18105951, 18376954, 29030131, 140818146, 155425281, 1939095186, 2504856858, 3718959709, 9038568331 86 | (none under 10^10) 87 | 274, 45169, 880635638 88 | 111, 183, 5289, 45399, 158177, 640118019 89 | 292, 424, 568, 851, 892, 1099, 3887, 6179, 10363, 25645, 26966, 113869, 177085, 344924, 1138216, 1238005, 2162518, 4513304, 11778964, 1378324105, 3521782328, 6742881758 ---+---------------------------------------------------------------------------- 90 | 31363, 279917, 406369, 1355369467 91 | 141, 1230, 2853, 6030, 6390, 34110, 285126, 405086, 655110, 931110, 3327370, 19108010, 22842069, 98598270, 100638190, 105731970, 127242783, 147479870, 307842242, 320952301, 811648710, 1426205849, 8651841582 92 | 204594571 93 | 134, 742, 9058, 18604, 29788, 10821299, 27648628, 238284508, 1584655642 94 | 119, 123, 255, 363, 465, 2895, 14883, 15659, 22245, 24645, 44455, 63283, 117905, 134783, 190005, 13271565, 82204095, 399555935, 433955523, 629242197, 1616051503, 2017770843, 3071443353 95 | 209, 266, 518, 551, 598, 2158, 4661, 4829, 9842, 41078, 60458, 116369, 608399, 1904294, 6998726, 28170674, 90325031, 248049769 96 | 53801, 755542669, 832053101, 893871643 97 | 132, 147, 258, 352, 372, 777, 1212, 2064, 2136, 2544, 4092, 4557, 10852, 25932, 27348, 29872, 62853, 62864, 108717, 115616, 273522, 402663, 455973, 895092, 1293072, 1738824, 2231529, 4014717, 4873376, 5307121, 7105692, 7434516, 7453392, 8336144, 11953768, 12578672, 13306812, 22097481, 27809232, 69138237, 88478552, 180607272, 264736032, 274659132, 289753112, 345702184, 707648456, 929659992, 1036801959, 2008285212, 2623943292, 2890944048, 3968159712, 4897223904, 5170696212, 6682736492, 8166094368, 8243338592 98 | 868543, 34709273, 118001503 99 | 262, 3095, 16325, 1653922, 50719715, 83575325, 360256691 100 | 711, 2253, 12449, 154761, 185501, 1894479, 11480661, 2305968213, 4033876773, 4084654401 ----+---------------------------------------------------------------------------