67^n=c mod n (2 <= n <= 10^10, 1 <= c <= 100) c | n ---+---------------------------------------------------------------------------- 1 | many 2 | 5, 13, 371, 445, 665, 5905, 130723, 434785, 4194785, 7150859, 15011045, 49684399, 527991685 3 | 95, 3215, 4486, 5587, 25418, 34535, 1055213, 3355318, 28664899, 2353273355 4 | 7, 87, 10371, 339299, 381721, 423914809 5 | 31, 38, 118, 124, 404, 6436, 4959217, 51299764, 152306173, 768398938, 914441596, 1078117076 6 | 61, 85483 7 | 25, 166, 213, 345, 354, 1059, 3246, 3945, 5358, 16525, 31225, 1158582, 2833998, 9032565, 12367282, 19445982, 66212079, 70096602, 85121689, 166922003, 1496724582 8 | 59, 16999, 698549, 6750625495 9 | 10, 14, 29, 56, 104, 190, 518, 728, 874, 2870, 3848, 4472, 4492, 6430, 8972, 10510, 11174, 30212, 41374, 50836, 69070, 87206, 93304, 135964, 213844, 234284, 328990, 367484, 540662, 1284610, 1470538, 1496456, 1527656, 1936424, 2110426, 3689861, 4665182, 5757464, 5827016, 6200344, 6710636, 6877810, 8328008, 10986004, 13029044, 21848372, 23966524, 29997170, 34926008, 42553784, 50970830, 57329798, 58649270, 63215470, 74323672, 85264244, 103137524, 156105404, 158257736, 192708088, 207801842, 218866388, 269644604, 278125630, 383466044, 406034252, 409762346, 607755512, 673964270, 727820756, 820399036, 840149876, 915594212, 1107143956, 1572240488, 1792808024, 2679757330, 2876997934, 2919890030, 3022315844, 3418780817, 3708779576, 4481055644, 4706546710, 6563029030, 7946575826, 9172112558, 9745022270, 9797011910 ---+---------------------------------------------------------------------------- 10 | 19, 141, 237, 6739, 49509, 462039, 39700607 11 | 91, 4478, 462007, 1671922, 8724079, 14944459, 19236511, 25146659, 3830705641 12 | 451, 2321, 143131, 7910179, 13807453, 122738645, 701277223, 8305223023 13 | 15, 215, 556, 636, 746, 1203, 6036, 16108, 183756, 9691068, 23620273, 25380655, 26165215, 41631477, 76606251, 226549348, 694705786, 1988457846 14 | 53, 482859779, 1272077759, 3751073309 15 | 4474, 122249, 6596287, 13590494 16 | 17, 51, 119, 2193, 2429, 17691, 83037, 2733521, 8201847, 9322817, 15392613, 147400999, 418163029 17 | 26, 86, 152, 494, 716, 7036, 84185, 212654, 390556, 4314788, 103180006, 675062545 18 | 49, 175, 343, 395, 8575, 8611, 27097, 85450955, 167470975, 5084523955 19 | 30, 90, 298, 1370, 4530, 5310, 8310, 12531, 109290, 187690, 203430, 1762191, 4662583, 6158319, 7705807, 10713270, 10826370, 52653570, 134012418, 252289854, 2755122218, 8989834830 ---+---------------------------------------------------------------------------- 20 | 47, 1492854427, 1629346769 21 | 23, 1660, 2234, 271820, 806044, 1553033, 4925671, 5093188, 76301332 22 | 105, 1285, 1659, 3713, 42963, 92165, 5463245, 26887281, 32961685, 77239785, 206159585, 1524344097, 9844140477 23 | 35, 55, 58, 77, 286, 295, 803, 3718, 5434, 9802, 12298, 22286, 25355, 26495, 62195, 101606, 132415, 770693, 1531783, 2301442, 13045318, 15865498, 18480329, 36800687, 38984935, 50712706, 61325957, 212060354, 219707939, 598745554 24 | 43, 4469, 41539997, 130423829, 3478116967, 9632923991 25 | 28, 62, 76, 78, 236, 248, 276, 428, 492, 696, 808, 824, 1102, 1288, 1446, 1788, 1794, 2632, 3892, 4963, 6454, 7052, 9096, 9628, 9816, 10664, 12872, 20996, 28984, 31864, 64452, 70104, 117218, 150369, 167606, 229242, 238588, 742188, 902274, 1030412, 1083468, 1123286, 1148492, 1238543, 2196344, 2387298, 2683544, 3327788, 3569188, 4660852, 4880344, 5029576, 6263404, 7456802, 8090908, 9344072, 9918434, 10133512, 11655596, 11804334, 12684146, 13335332, 20563566, 21562258, 22719918, 24444868, 25841716, 29872362, 30573508, 33949924, 34435986, 69569608, 86011932, 102599528, 112766468, 115404978, 126295852, 132258658, 152118744, 168747074, 204153416, 230665738, 236151202, 300851272, 304612346, 321525192, 394642326, 683121124, 942825016, 1287800636, 1427500772, 1536797876, 1818624678, 1828883192, 2156234152, 2435592872, 2500038152, 2873119228, 2963001612, 2968650286, 3547115666, 3788149532, 3972161378, 4636588218, 5820446122, 6006463224, 6203905163, 6274051052, 7865946276, 8440713516, 9494285332, 9827258492 26 | 41, 10807 27 | 46, 194, 205, 14545, 6667586, 13591661, 3411493051 28 | 123, 135, 489, 2619, 12195, 15489, 166995, 942335, 2789463, 9283095, 755205757, 841608763, 1214338095, 1674803817, 1843638939, 7228423197 29 | 52, 446, 530, 724, 8564, 760924, 116476670, 124298854, 1476397210, 1586782132 ---+---------------------------------------------------------------------------- 30 | 37, 69701, 3501827, 483422987 31 | 57, 741, 1486, 3957, 124449, 142077, 1505586, 1803706, 4129707, 17924259, 637717197 32 | 65, 505, 2225, 3325, 15665, 22025, 29525, 328225, 1960225, 2173925, 12100805, 20973925, 55089685, 59195285, 75055225, 260709925, 292721267, 484281065, 1286584445, 1406857985, 1859136025, 2639958425, 2987504081, 4031478025, 4044818665 33 | 148, 493, 1114, 1235, 2533, 6896, 49799, 136156, 136391, 139292, 505564, 662176, 4047095, 4733651, 5961611, 6571715, 23902931, 35085637, 75729169, 177581776, 926289886, 1389594896, 1398081095, 1581890606 34 | 39, 957, 1843, 1947, 2103, 5709, 13101, 30327, 311541, 737143, 2044163, 10659913, 25117433, 25424751, 50631187, 171961667, 230856911, 246655299, 1568601039, 1589459289, 3326014263, 4281605493, 5325563451 35 | 262, 4318, 102442, 274073, 52162969, 118205726, 138400133 36 | 660243953, 1822509889 37 | 45, 106, 171, 916, 1043, 1545, 1778, 16707, 29332, 33678, 71372, 78428, 117405, 455508, 1192545, 10086745, 28575297, 28824183, 44710047, 491921443, 653271899, 1665018324 38 | 5095, 19517, 471773, 1157635, 5392115, 6122689, 6624755, 9703835, 1069921679 39 | 70, 178, 12890, 32410, 61730, 78610, 395290, 540263, 1131151, 1792733, 3375770, 4074910, 367476470, 642921349, 1886683330, 7231841458, 9660173278 ---+---------------------------------------------------------------------------- 40 | 177, 5097, 820531, 1841977, 488207463, 1696821073 41 | 278, 481, 10820, 32104, 527080, 2015108, 4431320, 6555209, 53648180, 57554620, 69540140, 75889720, 108433340, 862804813, 1841333126, 3738563720, 4047522328 42 | 76705, 220739, 2337427, 1350125065 43 | 75, 537, 654, 9051, 12075, 24675, 33621, 66255, 1741686, 2992098, 3081435, 3233438, 3772014, 13711575, 31252895, 118556202, 725810618, 1092538734, 1304635498, 1791664521, 2158924891, 2696801475 44 | 8778581, 719640139, 751800329 45 | 202, 253, 1342, 10324, 36181, 245836, 1831916, 2061191, 4089076, 11025916, 32548703, 47596637, 115064422, 135911044, 197189164, 1551436777, 2068854997, 3891605036, 5487164419 46 | 679, 6441, 16407, 100239, 2657553, 12770181, 15871347, 31911147, 129956311, 589699223, 4083790497 47 | 4442, 337531265, 4702384594 48 | 223393, 561260339, 2950867679, 6750625295, 7844421955 49 | 50, 74, 114, 130, 150, 184, 232, 332, 426, 456, 690, 708, 1124, 1450, 2118, 2850, 5244, 6024, 6492, 7134, 7890, 9498, 10716, 17284, 18908, 20676, 22282, 27274, 33050, 38350, 40984, 54650, 62450, 86710, 131774, 150357, 180150, 337070, 367256, 470130, 475824, 486632, 592150, 600806, 639312, 673672, 847554, 876136, 880116, 892734, 926488, 993282, 1085228, 1094312, 1126626, 1212144, 1612470, 1820774, 2317164, 2959150, 3142950, 3536670, 4672968, 5465274, 5543672, 5667996, 5876777, 6384912, 7013850, 7989470, 14276450, 15001390, 15048344, 15391536, 15752976, 18065130, 19687692, 22072208, 24734564, 29513368, 38891964, 39944530, 42807890, 45696344, 47730810, 65766142, 84024656, 98688070, 105216350, 132424158, 140193204, 154647056, 170243378, 222615768, 261649616, 269257808, 287370070, 333844006, 376294470, 495209942, 594928550, 738407452, 764016150, 777716454, 1050906288, 1175640434, 1236865016, 1434181790, 1502631150, 1618030410, 1931150992, 2003756978, 2746398288, 2825214648, 2870417450, 2939659746, 2993449164, 3055737512, 3718608230, 3873793416, 5127622923, 7777896150, 8503306050 ---+---------------------------------------------------------------------------- 50 | (none under 10^10) 51 | 634, 117277, 22493539 52 | 485, 5893, 21629, 32905, 46185, 300711, 374565, 494057, 6322763, 466873599 53 | 133, 2218, 16534, 2878724, 3375312635, 5270954815 54 | 801676801, 5163897973 55 | 1478, 12582, 22879, 25059, 150966, 959661, 8856189, 11688678, 41001678, 115164207, 273644054, 1290477039, 1686395523 56 | 341, 5549, 7037, 14663, 37169, 22415437, 53396849, 336059977, 472474937, 663315043 57 | 125, 452, 554, 89164, 604925, 2040062, 7029158, 8110316, 18824411, 25573748, 130586825, 135012505 58 | 1295, 35315, 60141, 1306655, 21723695, 26747855, 114269109, 229728201, 271794255, 1362976255, 1748642231, 3373297671, 3913628033 59 | 886, 1510, 14330, 5935810, 428715107, 531313870, 1597950446 ---+---------------------------------------------------------------------------- 60 | 226739, 3167677, 4104856867 61 | 69, 82, 260, 940, 1052, 3869, 5108, 6537, 23860, 78140, 150351, 274321, 275514, 420836, 769317, 825002, 1573692, 3418764, 5041798, 194472780, 418568217, 888914140, 1256947268, 1993655980, 3506192124, 7568318420, 9753425740 62 | 2545, 677653, 2652505, 4538531, 13797601, 4195149841, 7826404841 63 | 1786, 2743, 3154, 4426, 47865515, 53720407, 4632264671 64 | 111, 129, 261, 777, 1251, 5607, 8769, 13251, 19287, 31113, 55503, 130149, 150129, 158619, 237873, 714063, 1017897, 1145163, 10177923, 36734781, 102826701, 127728543, 160291719, 166324053, 307287417, 336139383, 339920517, 749884293, 1271744427, 3826539021, 4760759253 65 | 116, 158, 224, 548, 928, 1268, 2344, 34784, 172576, 245312, 562778, 820448, 1145024, 1434944, 4712464, 8723776, 12088328, 173785328, 236635808, 1077086948, 1790535632, 8907075776 66 | 40929961, 132645229 67 | any prime 68 | 2675, 11255, 90658199, 94823375 69 | 170, 1604, 2210, 2510, 2956, 32470, 61948, 67490, 132170, 161330, 617732, 645388, 4951778, 38346170, 785755958, 2611276804, 5521852130, 7367457110 ---+---------------------------------------------------------------------------- 70 | 339, 2661, 593697, 2849449, 3333837, 6185659, 17866173, 57992181, 240015009, 1129686753, 9301715553 71 | 94, 377, 4418, 1012246, 4212221, 452326873 72 | 2951, 32165, 4381805957 73 | 195, 333, 436, 552, 771, 1278, 1359, 1524, 2655, 9992, 15327, 30812, 50115, 313755, 393464, 470895, 1079955, 1551948, 2562156, 12625695, 18024462, 29014515, 43003881, 45435035, 54631284, 96534584, 112809492, 187553544, 251666586, 284170968, 309892131, 348786531, 1011822012, 1125104195, 1256366418, 1770827804, 2918578167, 3018766635, 4196189412, 4666173135, 5595020664, 6106958918 74 | 100697 75 | 4414, 2515846, 44191846, 930388654, 2448333238 76 | 219, 4119, 73803 77 | 2206, 89884, 2382476, 2565749, 6554005, 20151044, 25131116 78 | 7255, 122359, 374891, 17176199, 195930295, 3797058955, 5607250451 79 | 98, 161, 602, 1358, 4214, 9359, 13774, 75171, 130487, 132590, 184494, 249654, 295883, 434802, 1586071, 5950070, 7662030, 10441623, 12956846, 24351090, 46329941, 53132219, 1267335690, 1483716710, 7995820159 ---+---------------------------------------------------------------------------- 80 | 169, 315289, 12970327, 830373661, 1319006561 81 | 112, 208, 280, 364, 380, 424, 464, 520, 692, 820, 1036, 1456, 1544, 1576, 1720, 1748, 3640, 5740, 5960, 7696, 7720, 8944, 8984, 9160, 10360, 10660, 12860, 12880, 15340, 17944, 21020, 22348, 23014, 27820, 28048, 29380, 30340, 43108, 52880, 60424, 68720, 74620, 82748, 87640, 91024, 92660, 100360, 101672, 109144, 109876, 129946, 138140, 166640, 174412, 182320, 186608, 271928, 303856, 334516, 343720, 373360, 427688, 449296, 468568, 539632, 657980, 667702, 732260, 734968, 1081324, 1151912, 1314460, 1390588, 1488760, 1496872, 1504048, 1564072, 1648720, 1833328, 1895120, 1905320, 1949668, 2381320, 2569220, 2715076, 2760940, 2927440, 2941076, 2992912, 3055312, 3074180, 3157480, 3529456, 3628706, 3713320, 3840818, 3872848, 4220852, 5241496, 5461436, 5619440, 6172660, 6311120, 6796720, 7379722, 7436260, 7651268, 8289736, 9098440, 9107312, 9330364, 11025052, 11514928, 11649416, 11654032, 11921224, 12400688, 13421272, 13755620, 13771282, 14089096, 14469886, 14614756, 14839588, 14898440, 15304880, 15466120, 16656016, 16877072, 16960060, 20631760, 21291460, 21308560, 21972008, 22982440, 26058088, 29624140, 31958636, 39842920, 41086396, 43696744, 43760080, 47157832, 47933048, 55921060, 56715752, 57745240, 59839436, 59994340, 67627144, 68853460, 69852016, 70499260, 76467016, 78301840, 84963440, 85107568, 95314960, 99623780, 101941660, 114659596, 117298540, 125392852, 126430940, 127222180, 128961680, 131993680, 136578988, 140383180, 144122332, 148647344, 152342180, 153877360, 170528488, 188808040, 206275048, 211276468, 225041620, 239025548, 273028420, 281765698, 302298808, 312210808, 312816868, 316515472, 340335268, 352363780, 362409224, 385416176, 387833588, 392712176, 399681520, 407932520, 410111920, 415603684, 437732776, 539289208, 543919240, 556251260, 616828240, 624913928, 625383304, 628927480, 766932088, 781976840, 812068504, 819524692, 862586920, 956421968, 958806940, 999730060, 1043605172, 1075996616, 1099702708, 1147819304, 1171080820, 1188424520, 1190266480, 1215511024, 1347928540, 1455641512, 1480975912, 1494952420, 1503952360, 1564391768, 1640798072, 1680299752, 1831188424, 2070834320, 2214287912, 2309352040, 2376076144, 2887580248, 2988316396, 3144480976, 3171242620, 3340786540, 3344959556, 3585616048, 4118860720, 4131751220, 4524501640, 4968942160, 5108868040, 5359514660, 5528738020, 5753995868, 5839780060, 5872269520, 6044631688, 6117282740, 6359934640, 6403612406, 6713384080, 6837561634, 7410436940, 7417559152, 8136732760, 8320506376, 8375039920, 8416431620, 8962111288, 9183721456, 9413093420, 9616206472 82 | 225, 405, 1269, 1525, 2025, 44085, 100227, 1052325, 1074573, 1525565, 3562705, 4916685, 5749041, 17238885, 68930305, 867850083, 2433957525, 4854186873 83 | 115, 2726, 4406, 141630158, 7916139667 84 | 221, 3287443, 795846701 85 | 92, 734, 1491, 4074, 10481, 21477, 60207, 88158, 97348, 323484, 401916, 519829, 12431026, 14689252, 37626141, 52364759, 57970916, 61075749, 169824836, 989735187, 2849052738, 5300059191, 6461313006 86 | 203, 494711, 312162641, 355577033, 5476621493 87 | 142, 4898, 77765, 663390545, 2819580758 88 | 633, 721, 2235, 17635, 28635, 399171, 50366333, 65229711, 452836379, 8336872327 89 | 110, 247, 2332, 4351, 8104, 15290, 72127, 136664, 146170, 223564, 291064, 408353, 915956, 1001608, 4051982, 5652484, 11172970, 144468571, 161962427, 420148210, 493018070, 547040230, 715607090, 1250963348, 1388767490, 1504709756, 5133336472, 9125780161 ---+---------------------------------------------------------------------------- 90 | 893, 780277, 5514363733 91 | 318, 1466, 3558, 12267, 158043, 452943, 492321, 959394, 4064381, 11602314 92 | 145, 83849, 2058391571, 2611417819 93 | 314, 2135, 6167, 15575, 3487001, 4463123, 6888044, 20151028, 46596395, 119906012, 1273541675, 1469704415, 3973615475, 5742403061 94 | 159, 183, 1371471 95 | 1582, 153502, 25851857, 43729538, 3778498507, 5518638002 96 | 31351, 114271, 163142033 97 | 122, 212, 258, 356, 376, 872, 2064, 2705, 4272, 7584, 11274, 81528, 111471, 150333, 279894, 359021, 441824, 1129143, 7766768, 8559776, 10832047, 11324449, 11608805, 380293885, 826405728, 1100884024, 1338562581, 1398546192, 5090136288, 8961534798 98 | 3379, 148559, 4144897, 355296055 99 | 878, 102538, 4236850, 17819029, 28511650, 48205967, 63911509, 71671090, 751537351, 2815547102 100 | 473, 657, 2979, 5013, 8657, 9111, 19053, 97817, 182853, 845361, 2297979, 4744169, 13173787, 13806813, 119023267, 143496859, 183769947 ----+---------------------------------------------------------------------------