71^n=c mod n (2 <= n <= 10^10, 1 <= c <= 100) c | n ---+---------------------------------------------------------------------------- 1 | many 2 | 3, 23, 159, 6753, 30118741, 174858961, 708425141, 823699713 3 | 17, 22, 242, 458, 2827, 578017, 21071182, 102179551 4 | 67, 53237, 238513, 36372319, 177859987, 219493063 5 | 11, 724, 2518, 12441, 140396, 178953, 458133, 95044521, 5402781681 6 | 13, 145, 1405, 1769, 2353, 221405, 404435, 3532477, 3705535 7 | 114, 1678, 1902, 182299, 3138673, 6500874, 21268518, 30050677, 597115102 8 | 9, 21, 39, 57, 63, 69, 399, 477, 651, 819, 1267, 1281, 3787, 5031, 5187, 7299, 12831, 16911, 17841, 18321, 20259, 22971, 36027, 103593, 173979, 325143, 360867, 685447, 910191, 914907, 936453, 3500241, 3844281, 4619979, 7407787, 7981113, 9670791, 10320247, 12521957, 22381983, 29528679, 31086291, 60208053, 64951587, 87946257, 90356223, 146794323, 191453367, 237661671, 247004931, 253021101, 311358567, 360375483, 393042819, 427985229, 442285401, 524576883, 671381763, 1007566287, 1366392531, 1737435021, 1815008913, 2125275423, 2403782199, 2471099139, 2969489271, 3586385109, 5025742971, 5304765219, 6002866021, 6393062277, 7635571293, 7639404897, 9314034651, 9725237571 9 | 31, 34, 44, 52, 74, 376, 388, 484, 916, 1016, 1144, 2392, 3404, 4114, 5654, 11128, 19076, 43108, 53687, 54686, 70754, 74899, 111416, 183658, 379544, 400184, 529913, 577496, 1156034, 1462708, 1530034, 1760356, 2162696, 2190914, 5344018, 7300996, 7714418, 10031986, 16705156, 18511016, 20144344, 35967404, 42142364, 73073474, 173763304, 204359102, 265662436, 284415352, 364846616, 469354583, 837188056, 984157724, 1192294004, 1206000706, 2151301834, 2652307724, 2866053112, 3454149814, 4821174572, 6162314258, 9157263058 ---+---------------------------------------------------------------------------- 10 | 61, 1815421, 3761347, 301427417, 351558797 11 | 15, 1006, 3579, 19955, 167990, 8511626, 150352445, 5712062135 12 | 59, 266309, 9130244621 13 | 29, 68, 838, 498268, 4240276, 4874308, 7576084, 60280721, 73537158, 894638267, 4101917284, 4894351764 14 | 19, 3713, 69441, 357897, 8540043 15 | 718, 31109, 2295083, 3467513, 4068218, 29329202, 43268761, 55494086, 114167294, 351173074, 3761309398, 5382418211, 6159372821 16 | 185, 851, 39337, 32758331, 36031843, 48762955, 77363669 17 | 76, 177, 314, 688, 1011, 8703, 29151, 334364, 692213, 150980528, 208702544, 887395006, 2274308327, 3766373456, 4002463756, 4299366224, 7048806243 18 | 53, 1333, 3139, 30733, 561193 19 | 62, 169, 33241, 46478, 227694, 569034, 1735007, 2003502, 2877482, 39357257, 126845486, 2699390282 ---+---------------------------------------------------------------------------- 20 | 357891, 1843809, 3783511, 1674926009, 2093349639, 2396103657 21 | 305, 502, 1948, 8455, 10436, 61774, 200659, 589340, 1013470, 11672812, 14788765, 19902140, 34001876, 35583637, 974464684, 2947981930, 7473674851, 7797416420 22 | 133, 5873, 54551, 73213, 6223661, 9360281, 302391403 23 | 26, 338, 386, 494, 699, 129082, 5374538, 10898247, 23581479, 116314694, 250317818, 6014357031 24 | 47, 2310135467 25 | 38, 78, 116, 132, 276, 1448, 1794, 1992, 2552, 3322, 5036, 5172, 6312, 7654, 8382, 11324, 12072, 13308, 24882, 37228, 41298, 73092, 77468, 214314, 249866, 280792, 309894, 357906, 632498, 822876, 916266, 1074392, 1241494, 2246946, 2254902, 2652222, 2722746, 3856471, 5161026, 5200026, 5605788, 7445082, 7744628, 8791242, 10079528, 12079002, 12088542, 12849492, 17592042, 33882248, 36717346, 40065338, 55138712, 61716988, 103322692, 114969768, 123406042, 189334968, 190089042, 215935302, 256458948, 299346456, 345777522, 661818602, 856883192, 1065821592, 1277719482, 1290117658, 1479176492, 1506269942, 1830667548, 2006725354, 2472055854, 2665397514, 3553691502, 3802846612, 5236757364, 5636458952, 5794888168, 6357955244, 8893857642, 9283540776 26 | 27, 33, 45, 75, 135, 225, 555, 675, 723, 2005, 2061, 3975, 4525, 4983, 30105, 72483, 84933, 99985, 232083, 233307, 1792263, 2046195, 2660039, 12283387, 25469075, 33902775, 49064775, 142870043, 222259025, 236414925, 648871035, 1185421395, 1414374579, 1544582475, 1926596799, 7396456759, 7570520955 27 | 46, 121, 218, 1817, 3091, 1404931, 2803799827, 8047616951 28 | 43, 79292933 29 | 358, 596, 6839, 8299, 24364, 25563, 29869, 259203, 393533, 474329, 519428, 971404, 10467982, 17361812, 23098929, 28405547, 52977988, 95108428, 160450948, 837380572, 1014647852, 1113021587, 1212448207, 1551538751, 1584307556, 2370894037, 3677314004, 4223935508, 4697569394 ---+---------------------------------------------------------------------------- 30 | 41, 2623, 2086260259 31 | 334, 20765, 31938, 54305, 159990, 162349, 4809730, 4813086 32 | 31993, 357879 33 | 136, 592, 626, 1072, 3184, 3424, 6856, 9916, 85579, 1588228, 1973284, 2787989, 3619831, 4436128, 21689968, 29851783, 49320223, 163356272, 1887772888, 2051544709 34 | 37, 7363, 2661889, 1827402061 35 | 279, 2987, 5006, 7719, 29823, 50499, 55149, 58221, 153207, 169959, 686677, 2027019, 18667582, 118536549, 260234818, 403032519, 5971549049 36 | 77, 161, 469, 2555, 3535, 24545, 24955, 25445, 52505, 64015, 87265, 109585, 1671985, 8456335, 24755687, 69350135, 107310721, 177221149, 225455545, 732790555, 1392160157 37 | 143, 198, 278, 428, 611, 1494, 1649, 1692, 2932, 2948, 23466, 76932, 340428, 445148, 661236, 1315908, 5458974, 7301778, 12987018, 13545323, 45723252, 339455358, 413090892, 540929034, 2108598722, 5775307758, 7469562356 38 | 357873, 1821899361 39 | 82, 122, 199406, 4126322, 138391837, 6111182549 ---+---------------------------------------------------------------------------- 40 | 34691, 1367596597, 7026112531 41 | 65, 237, 365, 453, 635, 1003, 2495, 29545, 111647, 296330, 1110665, 2541164, 4118984, 4709895, 9884216, 11356910, 56466169, 250839928, 339799665, 442046740, 553945580 42 | 149437, 630953 43 | 742, 3682, 6986, 7462, 77358, 90766, 206794, 661822, 799494, 1419378, 8512582, 60831701, 134267574, 139798722, 141924194, 8854811018 44 | 51, 117, 7017, 1183251, 27249433, 6124388673 45 | 164, 356, 2498, 6964, 423284, 511844, 47531129, 431095498, 2902674338, 7972811876 46 | 3835, 277595, 882845, 1344655, 81349099, 1804229305 47 | 93, 111, 454, 1443, 9867, 10519, 265397, 12664101, 43849573, 223793427, 1055579767, 2086744297, 3104010327 48 | 583, 67037, 341693, 2030163223 49 | 66, 102, 174, 176, 184, 228, 296, 912, 962, 1392, 1798, 2524, 2678, 2706, 3356, 3804, 5016, 5174, 5358, 6556, 7088, 9691, 10104, 10763, 21774, 24816, 56816, 80562, 134214, 134966, 169286, 193476, 244586, 252176, 294276, 314448, 349096, 364598, 445506, 489264, 499796, 591096, 915736, 1071024, 1104856, 1331688, 1556094, 1874902, 2029656, 2942288, 4208604, 4209176, 6277346, 6487486, 8339196, 8345136, 9010118, 13001748, 13571536, 17914354, 20007802, 22151608, 25575332, 27117156, 33625986, 36113144, 42537036, 50709466, 60101354, 79242596, 88306782, 94581386, 99657366, 105401928, 119533818, 124023192, 131837712, 187139208, 201277488, 220483866, 266707218, 473072998, 495273032, 497731512, 538797188, 747605064, 748572506, 752204604, 1099006184, 1194230204, 1347042232, 1364235234, 1599895778, 1782583928, 1801113256, 1880190989, 1905030982, 2212761386, 2569575756, 2680954644, 3807984136, 4089025146, 6486663356, 7772864248, 8229812646 ---+---------------------------------------------------------------------------- 50 | 147, 299, 301, 1311, 2107, 51123, 98763, 386267, 1069719, 16870357, 39476507, 39827739, 139292321, 201721247, 219646257, 236139371, 387782619, 7587252561 51 | 998, 28937, 9282635, 90211465, 251190575, 661786042, 1313806825, 1751568890, 1795676450, 2773387235, 3716946070, 6723433127 52 | 883887079, 937871681 53 | 58, 86, 99, 141, 6627, 8074, 52029, 67419, 754713, 2310148, 47671363, 121847487, 147433604, 295043159, 464153031, 475220817, 548994974, 636102158, 8284034169, 9176842334 54 | 197039, 41777573, 47213777 55 | 554, 3798, 7578, 11183, 14814, 18006, 19518, 24678, 55026, 856582, 1598958, 22525506, 219996618, 281795057, 869114998 56 | 85, 155, 165, 2805, 4565, 71571, 103745, 167255, 222179, 398805, 1104239, 2249237, 5952155, 6202857, 22790735, 39781173, 546509235, 2419029085, 2905131315, 4078920835 57 | 172, 178, 203, 244, 328, 692, 959, 6184, 8204, 43211, 100312, 147644, 185423, 232136, 1821113, 7038424, 8071931, 8643194, 11551009, 14396248, 14749448, 22952104, 27105326, 28706863, 47463448, 53136328, 80520244, 98461174, 135193709, 136779944, 139700876, 1513461496, 1756535059, 2424330328 58 | 187, 1261, 46057, 3548511809 59 | 94, 106, 247, 8133, 9823, 202058, 516153, 3527738, 402375559, 2711356923, 7418203573 ---+---------------------------------------------------------------------------- 60 | 28831, 91292531 61 | 166, 470, 7620, 13830, 130316, 527998, 707990, 1955570, 2118220, 9928860, 13172455, 37060516, 73644132, 272704890, 419085078, 902114645, 4089085874 62 | 3789, 119283, 207231, 427569, 1027629, 5488292913 63 | 262, 1763, 313693, 3426877, 13228598, 35042666, 98806394, 1571257883 64 | 59647, 88339853, 1067377087, 1124294939 65 | 129, 219, 622, 632, 4161, 5734, 16473, 29116, 161264, 178923, 578379, 917408, 1132491, 1374944, 2792103, 3176452, 4495168, 6087927, 6095702, 7426607, 13594432, 283942479, 312895456, 603098931, 1884494624 66 | 72005, 125285, 1260335, 1483271, 713465185, 2665477861, 4626818135 67 | 377, 1658, 6844721, 165884899, 986867023 68 | 303, 3543, 20384467, 2123632747 69 | 226, 332, 83669, 112891, 306164, 71901086, 75631363, 216715972, 454643867, 1438244636, 2347836997, 9279530557 ---+---------------------------------------------------------------------------- 70 | 253, 1733857, 16409833, 96701693 71 | any prime 72 | 120271, 3342637, 4169503, 724255663, 1876352083, 2822010451, 4678492627 73 | 534, 552, 2936, 4236, 11196, 11274, 16552, 34504, 63834, 77596, 121756, 182232, 288952, 1206246, 1411756, 3337272, 4640994, 6629544, 8290042, 9088682, 10499176, 29807748, 80230632, 124331346, 1902825608, 4314630988, 5602203576 74 | 543, 1977, 1896900783 75 | 382, 3179, 24382, 34894, 919577, 8374399, 39201527, 127776718, 373843418, 394755238, 1533186314 76 | 1585, 2795, 74275, 1138315, 3759275, 4810237, 5830175, 3184818775 77 | 146, 1796, 7779, 56596, 8531948, 207071979, 318702308, 371272849 78 | 12019, 25291, 78352861, 89776127, 359599919, 2517331901, 3096979207, 7094038639 79 | 606, 1654, 80646, 93959, 94362, 443922, 2867803, 3919471, 1180726962, 1622512487, 6770356279 ---+---------------------------------------------------------------------------- 80 | 81, 87, 221, 297, 493, 1371, 2781, 8109, 26477, 42201, 122067, 184497, 420957, 854961, 2247831, 4261053, 9629037, 23529497, 49212153, 64891989, 168491367, 859079817, 931649967, 1694846967, 2410179717, 3320489997, 7555374387, 8472684077 81 | 88, 104, 148, 190, 230, 260, 340, 404, 752, 776, 820, 884, 890, 968, 1040, 1160, 1480, 1832, 1972, 2032, 2288, 3088, 4784, 6028, 6032, 6808, 7270, 7460, 8056, 8228, 10088, 11120, 11308, 12934, 13940, 15440, 15580, 18668, 20470, 21460, 22256, 23260, 34480, 37810, 37876, 38152, 47444, 49880, 52676, 63760, 65936, 70120, 86216, 91460, 105908, 107374, 109372, 133370, 141508, 149798, 155108, 177692, 181220, 200720, 222832, 224818, 241240, 242840, 259376, 343804, 362960, 366920, 367316, 373648, 378380, 435236, 447760, 449384, 539510, 581060, 592756, 701240, 759088, 794728, 800368, 818320, 955760, 970220, 990490, 1015508, 1059826, 1154992, 1220648, 1347320, 1462760, 1548020, 2312068, 2513620, 2560220, 2773328, 2925416, 3060068, 3082396, 3128144, 3434702, 3454190, 3520712, 4082780, 4325392, 4381828, 4491920, 4548290, 4696880, 5730140, 6105370, 6220588, 6333860, 6777460, 8763256, 10542740, 10688036, 11866244, 12394940, 13354480, 14259128, 14601992, 15428836, 18223820, 18403832, 18553460, 18760040, 20063972, 20329352, 21648820, 23718928, 24185380, 24348880, 28931432, 31540580, 33410312, 33726520, 37022032, 40288688, 40690408, 50547472, 52221488, 52362740, 65707420, 70824940, 71273380, 71934808, 76959760, 82328168, 84284728, 90642064, 93396980, 93617560, 117145552, 118922647, 120968860, 144549520, 146146948, 168109916, 177980720, 199010572, 204026960, 231776456, 234523640, 235540528, 262096636, 270567760, 278781220, 281851282, 299056190, 299931224, 321299780, 321550352, 323180156, 347526608, 383930518, 402349901, 402653584, 408718204, 501184820, 501303920, 524049040, 531324872, 568830704, 628971320, 642356482, 672532040, 729693232, 771421520, 774818872, 779763640, 852186124, 872358160, 902114635, 938709166, 1110089732, 1114014512, 1237406351, 1330393328, 1365750620, 1480969880, 1674376112, 1738654180, 1827158840, 1879287058, 1968315448, 2040560980, 2162143756, 2324296294, 2358358096, 2384588008, 2412001412, 2502552260, 2573930728, 2594773064, 2618177420, 2868783356, 3040290032, 3050272784, 3170865752, 3343576808, 3676560040, 3777852572, 3854183842, 4107976084, 4129857520, 4208318740, 4209348260, 4302603668, 4857215528, 5304615448, 5710698040, 5732106224, 5838130220, 5986214608, 6602835980, 6602907268, 6908299628, 6940876904, 7433399944, 7689479558, 7734483658, 8005913380, 8844680624, 8940634660, 9370164143, 9642349144 82 | 25273721, 48078763, 147952429, 1505847059 83 | 134, 34142, 89457, 16662554 84 | 68846089, 1096024337, 1288157221, 3204465053 85 | 91, 92, 118, 266, 1246, 1603, 7516, 12236, 34466, 51908, 68908, 88039, 102767, 121457, 227606, 835086, 3212958, 3214234, 4103246, 5533878, 6758773, 10331202, 43880918, 52904971, 133562212, 1916209694, 2567923148, 5221859172, 9150020274 86 | 95, 195, 335, 1101, 24865, 42015, 556095, 916655, 3945065, 4907345, 6061019, 472783307 87 | 4954, 442382, 360653522, 4677282026, 7188217961 88 | (none under 10^10) 89 | 212, 292, 309, 579, 1238, 1816, 3123, 3284, 27592, 76364, 134702, 343503, 2015663, 3357987, 33626099, 83876872, 108154318, 118426249, 824798264, 1730922579 ---+---------------------------------------------------------------------------- 90 | 1648133, 65590253 91 | 215, 410, 530, 1343, 3690, 4670, 5030, 7505, 14830, 53090, 138170, 415067, 440423, 875990, 1072742, 1255734, 1987110, 2594910, 4357110, 4672727, 10489705, 13315901, 16998102, 24557989, 100701085, 146665810, 474396089, 719106030, 2794670374, 4511471490, 5962922262, 8540018922, 9081227130 92 | 2563, 4647, 23233, 27537, 68063, 190911, 2113627, 7963091, 51209627, 208287971, 585628959, 913439807 93 | 506, 2474, 100873, 1149173, 1337452, 1347356, 16311082, 72526751, 293502011, 950276981, 990505997, 1450218341, 1653727396, 7135600018 94 | 58731229 95 | 2631, 4946, 95374, 481858, 24601442, 146559139, 157523446, 4721521391, 4828365022 96 | 395, 15985, 13520113, 22838345 97 | 188, 206, 258, 264, 744, 808, 1272, 2064, 2848, 4512, 5748, 7368, 8184, 13904, 15958, 16288, 16944, 17484, 37344, 56456, 75858, 112496, 164384, 557744, 641072, 792004, 946524, 2273744, 13829064, 16729584, 20698824, 29802127, 40917216, 49744669, 75499496, 176918759, 238681918, 372384546, 599237384, 823356112, 978076704, 1103648664, 2009102414, 3664269744, 7817634264, 8375876088 98 | 207, 249, 1437, 540737, 21599829, 117994237, 466080039, 553248429, 688799373, 2480654853 99 | 706, 1513, 1862, 17234, 35378, 76391, 403606, 1138298, 1507849, 2235122, 2918342, 4727534, 6231289, 42274946, 58033633, 213470558, 361184698, 841799063 100 | 740374321 ----+---------------------------------------------------------------------------