11^n=c mod n (2 <= n <= 10^10, 1 <= c <= 100) c | n ---+---------------------------------------------------------------------------- 1 | many 2 | 3, 413, 1329, 6587, 11629, 75761, 925071199 3 | 118, 12359, 3183450047 4 | 7, 553, 10881823, 3206616167 5 | 39, 51, 58, 14636, 2149244, 2485587, 5798491, 767044947, 5040205901, 9481935178 6 | 155, 2015, 5195, 220769, 236795, 13312715, 1175125835 7 | 38, 221, 533, 1017066, 1771554, 11609826, 2451217981 8 | 9, 21, 63, 117, 273, 603, 873, 1239, 3987, 17451, 19761, 34887, 146601, 227283, 734409, 780831, 5616009, 13950261, 17883333, 55399419, 56381013, 146208717, 196881351, 367483599, 451096737, 1050870681, 2775213597, 2897080473, 8043678909, 8745546417 9 | 14, 56, 104, 124, 236, 644, 728, 1054, 4184, 4504, 5704, 8792, 9128, 18044, 24248, 24718, 123388, 140504, 202264, 250754, 565258, 3697106, 4701608, 7930642, 17348126, 17428366, 19487174, 46015402, 113178884, 181429976, 232327256, 287259944, 947904734, 1138543324, 2306650726, 2736840584, 2764312616, 3208034648, 3344845762, 3557732492, 3826431896, 6236850374, 6366900094 ---+---------------------------------------------------------------------------- 10 | 18659, 24360617, 1237332463 11 | any prime 12 | 8153, 3433093 13 | 92, 204, 212, 885774, 3356358, 4837452, 221665292, 819726036 14 | 1317, 18751, 14534633, 25659159, 29118293 15 | 106 16 | 35, 215, 535, 581, 10349, 50783, 89495, 7649164565 17 | 26, 219, 1328, 1828, 5176, 8144, 148051, 165656, 653872, 811417, 866391, 1315376, 26614256, 1178973837, 2897890971, 8797709331 18 | 49, 343, 220067, 1154587, 2153011, 19621097, 1381371103 19 | 34, 306, 611, 1926, 590514, 3931127, 9768707, 17431698, 21445153, 23213754, 2370078666 ---+---------------------------------------------------------------------------- 20 | 57, 69 21 | 68, 172, 340, 670, 7460, 9070, 51476, 78490, 80515, 213410, 517430, 1850419, 2600740, 4160293, 62181172, 324463690, 825621620, 1545102148, 1945357444, 3246680057 22 | 253, 3058429, 56511359, 63978983, 113900347, 1439156113, 2844217823 23 | 327, 88629, 10158602, 11188138, 11367503, 161239178, 9769207826 24 | 1271, 1853, 35681, 7423373, 147747169 25 | 28, 78, 102, 116, 1002, 1608, 2532, 3976, 6036, 7044, 8302, 9816, 19528, 25188, 29272, 41528, 76678, 125976, 183841, 240006, 247026, 412788, 447528, 555583, 630228, 743426, 840696, 1319878, 2887548, 3224536, 3963676, 4298488, 4971174, 7699308, 11596982, 14919302, 18542136, 26363996, 30708008, 34102558, 95312716, 102019688, 133686984, 165272986, 241395332, 283012314, 399741764, 428725464, 458114568, 505083864, 640127496, 782734088, 1250383758, 1534089894, 1714151396, 2054653204, 3454998648, 3719172792, 4807927096, 5358305892, 5645466628, 8244154104, 8835713362, 8930256484 26 | 27, 45, 75, 87, 95, 135, 225, 565, 675, 775, 779, 1065, 6225, 11005, 15975, 19575, 72825, 75615, 154575, 237925, 582531, 1134225, 3035915, 6236865, 26853633, 36154749, 52398837, 198741425, 441949155, 530792095, 558822975, 1085685565, 1207329925, 1338357975, 1566809775, 3927755311, 5987573775, 6364747261, 6792488055 27 | 94, 629, 38797349, 5424220097 28 | 1633 29 | 46, 52, 93, 1124, 1743, 60399147, 186023878, 239687133, 375839583, 434166692, 3352435553, 6894769953 ---+---------------------------------------------------------------------------- 30 | 161, 24289, 53143, 624407, 6003869, 8946959, 71616881, 1662224501, 3809301209 31 | 415, 485, 690, 790, 23470, 46630, 62410, 354306, 6268901, 312762202, 4370145365, 9298363926 32 | 1141, 1299, 12801683 33 | 44, 88, 136, 176, 332, 352, 1496, 20372, 99121, 131384, 143288, 330308, 1552562, 1815088, 2726504, 15831299, 19303064, 26584624, 43767112, 46841696, 58749724, 71345192, 117559024, 147371368, 194600257, 621006548, 1339499744, 3734184232, 3970066712 34 | 909589, 3915283, 7105979 35 | 86, 387, 74433, 255903, 6854499, 6964466, 121080287, 424845466, 646931834, 1889232727 36 | 161015, 4859191, 8828341, 1507243195 37 | 119, 282, 391, 1212, 2094, 4868, 7994, 53388, 294812, 2264454, 4498804, 19951291, 33052817, 267889956, 332584578, 938051866, 1104262884, 1567359708, 1607860643, 3786228612, 4374306839, 5743952982, 7206746916, 7473809862 38 | 1293, 179410107, 587593353 39 | 82, 2149, 179419918 ---+---------------------------------------------------------------------------- 40 | 673279, 708949, 4458378809 41 | 129, 292, 430, 2360, 3544, 8945, 15707, 23960, 27080, 38301, 89709, 93460, 96776, 575690, 1397685, 2360872, 3344235, 3546460, 17490878, 51811435, 57776636, 75399490, 78463960, 80367235, 97913720, 244499720, 478271865, 742255160, 759304365, 832445336, 1615829834, 2775139480 42 | 577679 43 | 4578, 5798, 8762, 48462, 253074, 287198, 687354, 1248954, 3281646, 4102854, 8872442, 19546158, 221940834, 2204461518, 5118470647, 8028018734 44 | 77, 99, 1287, 2343, 3101, 3311, 5797, 7313, 8881, 11847, 11919, 14643, 22873, 26789, 34013, 42911, 51447, 73347, 84359, 130119, 131751, 153801, 231707, 240903, 284911, 537887, 600483, 608059, 630791, 916267, 936077, 1027889, 1307007, 1578773, 1729299, 1771583, 2570139, 3042599, 3077481, 3331893, 3554807, 4371981, 7138659, 9677679, 19240823, 21171231, 28010003, 64514013, 86214831, 90561273, 142775127, 205421909, 228872853, 269325617, 524987151, 840831761, 999643293, 1013019627, 1679966183, 1927898241, 1999567829, 2359696911, 2558243259, 3439518951, 3510100103, 3642573111, 4128331897, 4418816127, 5464468659, 6089329631, 7362337047, 9098771193, 9935199659, 9942131793 45 | 164, 356, 893, 3287, 5084, 10298, 21356, 29684, 423284, 3419564, 3740036, 7060364, 58434842, 86180618, 141123467, 316451236, 388148804, 618616364, 3369324404 46 | 65, 12385, 181699, 1185835, 851476801, 3196525801, 6632154455 47 | 74, 321, 40478, 333782, 544101, 1263254, 1805054, 51208174, 334523438, 1162198929, 4200000158 48 | 3589, 36667, 73159, 3605317, 5022431 49 | 76, 304, 442, 1066, 1338, 1392, 1986, 2168, 2346, 2544, 3156, 5052, 8056, 14648, 14928, 14946, 16008, 19912, 23214, 29944, 56024, 71444, 98536, 188336, 197866, 427926, 431562, 527034, 541168, 775704, 842992, 2034132, 3010992, 3306832, 3543108, 3739188, 4015568, 4227792, 7217482, 9284988, 9552084, 18019432, 19057224, 19857018, 23219652, 28127046, 29821776, 30085456, 37978536, 39292584, 51995472, 54730842, 72973156, 98663464, 102124706, 102409492, 123545756, 147436372, 187524696, 194570632, 260602968, 316705528, 356450146, 388407336, 428717776, 456366938, 597983664, 651252808, 688049014, 711550766, 751824034, 874147949, 1139872738, 1160270714, 1237789648, 1474842756, 1651415442, 1656171724, 1777947272, 2061787944, 3773895248, 3818697936, 3961119306, 4056818782, 4902435962, 5106274168, 6042978156, 7722909336, 7892644912, 7962245904 ---+---------------------------------------------------------------------------- 50 | 147, 183, 8967, 9529, 46661, 771897, 1388667, 5747359, 7459927, 53658961, 63901803, 581691381, 719021247, 1448585627, 7449370807 51 | 115, 290, 350, 1775, 2950, 109075, 134582, 162575, 192395, 2970475, 4358975, 17245025, 27679705, 28542025, 53617970, 178878790, 271695410, 7900755926 52 | (none under 10^10) 53 | 213, 369, 2084, 3842, 10819, 87993, 103966, 141211, 359779, 2555054, 9585153, 238227598, 267631294, 293830369, 566000449, 708765572, 3761107924, 5472867167, 9200537122 54 | 12997, 43157, 2148178279 55 | 66, 138, 198, 341, 594, 2334, 3586, 157146, 2295094, 9916302, 14349558, 55394658, 74222599, 120801186, 188952146, 200656818, 266637558, 318787578, 613079742, 1112959346, 1489870734, 8288903249, 9513175482 56 | 345, 53665, 1080655, 9138435, 100586715, 185235315, 907756095, 1518963107, 2484275789, 7427697587 57 | 328, 1816, 7292, 23032, 206968, 29791459, 104006222, 754970239, 1805372636 58 | 3731, 5014919, 101545817, 121120727 59 | 62, 159, 255782, 668518, 1204779329, 1311954467 ---+---------------------------------------------------------------------------- 60 | 10817, 175415767, 288443543, 8893474261 61 | 85, 260, 1956, 2929, 3979, 4735, 5748, 5970, 7086, 7970, 29730, 30005, 425983, 601378, 1807990, 3260660, 5916270, 8039316, 8422620, 10015189, 25362140, 118741620, 200627411, 511869020, 579296940, 1802046460, 2961040079, 9830650668 62 | 141, 18153, 1169037, 535202869, 1350333447 63 | 1682, 6877, 18706, 382654, 862786, 3986978, 270337439, 1108385473 64 | 19247, 37259, 378803, 516743, 1045361, 1512191 65 | 224, 527, 633, 938, 1316, 3644, 3928, 15592, 78112, 82624, 96347, 203336, 358934, 9951764, 35425376, 115268909, 115357162, 170065184, 201790997, 336292192, 407019441, 495376472, 2550964448, 7084784167, 8385724967 66 | 1595, 14635, 20911, 113465, 30017009, 199161811, 359123105, 559286915, 790507805 67 | 91, 174, 6286, 7966, 13342, 16618, 61086, 138882, 372882, 1215298, 4211646, 790031767, 4080606334 68 | 361, 1263, 1387, 25130977, 77489011, 128720497, 372768717 69 | 806, 6313, 14572, 350813, 6642866, 14520868, 3685564766, 4379283974 ---+---------------------------------------------------------------------------- 70 | 1372229, 49464341 71 | 105, 230, 315, 861, 13415, 18890, 60735, 330705, 596990, 1527057, 1906695, 2406069, 3448095, 13687359, 19727505, 472684401, 620791847, 682090954, 1947494871, 4093944585, 6023045890, 8698692451 72 | 1769, 4907, 339953, 9957701, 2024761349 73 | 2428, 6894, 36906, 449908, 49376876, 71452936, 228689704, 296834423, 376230024, 460032827, 1363720408, 2968316514, 6715760952 74 | 1257, 1981, 7651, 3797457, 76419771 75 | 27421, 2454794 76 | 235, 325, 685, 26575, 672433, 730087, 19231225, 58214075, 239345675, 2627567695, 7030949603 77 | 627, 649, 1324, 1767, 6259, 12093, 19437, 41162, 78826, 231477, 472153, 820167, 2435037, 3059764, 3136964, 4082686, 4133697, 7340839, 11790273, 22881111, 47206631, 69729902, 333491294, 1915543894, 2406085574, 4514150157 78 | 12053, 1645051, 15632047, 36856133, 176642407 79 | 98, 833, 80654, 168098, 1771482, 6623179, 8515178, 35454022, 318604223, 428745277, 779333018, 1506065246, 5570293694 ---+---------------------------------------------------------------------------- 80 | 81, 417, 459, 5083, 8523, 10341, 35613, 82303, 206091, 223227, 392121, 829971, 2498931, 9648963, 140578071, 156293059, 324139239, 2244914811 81 | 112, 208, 248, 280, 364, 472, 520, 820, 1060, 1160, 1288, 1456, 1940, 2108, 2344, 2380, 3640, 4898, 5740, 8368, 9008, 9820, 10660, 11408, 15980, 17584, 18256, 21616, 23108, 28220, 30940, 36088, 37480, 48380, 48496, 49436, 53620, 62764, 74620, 77488, 80485, 80530, 115030, 147320, 180460, 190372, 198520, 206440, 211460, 230264, 246776, 257608, 281008, 360440, 370396, 392680, 404528, 486260, 500140, 501508, 796720, 984952, 1065752, 1130516, 1133530, 1293040, 1489940, 1542352, 1610540, 1630564, 2146160, 2307130, 2546440, 2613520, 3842020, 4654552, 5002820, 5193380, 5442380, 6598924, 7394212, 8074360, 9403216, 9746780, 10090420, 11399920, 11478460, 11756378, 14539420, 14959660, 15861284, 16448380, 16574110, 16716388, 22607240, 22814270, 25214180, 27252220, 29285128, 29880760, 31336240, 34696252, 34856732, 37500572, 37811020, 38974348, 41225108, 52905580, 55040440, 57568360, 58178840, 69868240, 90847720, 92030804, 98647540, 105764420, 122039260, 122809040, 136986620, 141814388, 145911440, 158521316, 158774980, 160419580, 165298588, 180107260, 226357768, 226610060, 233187598, 234944848, 235565422, 239877820, 247181410, 259377656, 276972955, 278524088, 292413628, 330146360, 342974224, 343613620, 362859952, 375986884, 382174660, 397243420, 398878948, 405191920, 407180920, 423636808, 424839688, 464654512, 531994060, 544652098, 574519888, 775433110, 867973132, 908754340, 959263240, 965358940, 1057517680, 1120604440, 1162003120, 1227051134, 1375534420, 1512199330, 1798568168, 1895809468, 2277086648, 2322868780, 2364020732, 2450494520, 2554984120, 2833061012, 2870302480, 2892289304, 2992917464, 2997183788, 3056497552, 3116721808, 3309897095, 3337073530, 3721188412, 3942336344, 3948689680, 3978938860, 4325531440, 4613301452, 4749176752, 5087566180, 5320736092, 5473681168, 5528625232, 5765784166, 5775254260, 6069584560, 6113112880, 6367777160, 6416069296, 6689691524, 7065875152, 7115464984, 7652863792, 7821704840, 8083142360, 8154406120, 8511238654 82 | 252943, 253335881, 2176471631 83 | 10526, 1476579, 27820767, 86620911, 106889023, 156009243, 283666431, 323358701, 493247429 84 | 4064065937 85 | 1932, 2724, 4494, 4852, 7363, 9228, 18463, 118627, 126534, 188646, 2568396, 43821949, 51179268, 239560842, 369158412, 394493518, 1254123292, 2587135362, 4856082252, 7404810569 86 | 249, 365, 9165, 4080705, 8005245, 16118265, 120150505, 450306471, 574067793, 6279234117, 6851976405 87 | 874, 1394, 231298, 1113058, 1757842, 2196914, 42784186, 66648922, 1162611266, 1548044353, 8046503954, 9416110573 88 | 979, 2123, 6347, 6853, 28787, 104209, 296161, 964843, 1224971, 2421067, 2937253, 3888817, 4159771, 7746827, 7859467, 10057267, 22043543, 23964787, 27972637, 37977709, 44267443, 333688249, 638134717, 1093105387, 2310155947, 4638643039, 7082993533 89 | 169, 261, 428, 711, 7412, 170521, 514611, 12497768, 214358792, 227708153, 281533653 ---+---------------------------------------------------------------------------- 90 | 15251, 7112123, 728195203, 3107420359 91 | 410, 522, 1602, 2515, 3690, 11890, 311730, 905902, 1234105, 210873370, 225398730, 575373490, 621885130 92 | 177, 3759, 9429, 203133 93 | 14548, 11494799, 484211587, 485728454, 1126228886, 2662520974 94 | (none under 10^10) 95 | 309, 322, 742, 14371, 49503, 40063198, 1932093742, 2789121693, 6310988023 96 | 40795, 160955, 46751735 97 | 186, 344, 404, 752, 1356, 2848, 2976, 14286, 15996, 22919, 51928, 65798, 69936, 131704, 261264, 288532, 335056, 378696, 456816, 475296, 737544, 939704, 2879068, 5723987, 7733032, 8223664, 19488864, 44184696, 116323734, 238362479, 249537788, 3774850279, 4932901536, 6943425612, 8107478688 98 | 411, 32292881, 2357947593 99 | 451, 5401, 41374, 548333, 885797, 4561561, 42487474, 102981817, 103230586, 123126623, 327098137, 1148506462, 1229104634, 3415066787, 4330974034 100 | 1971782729 ----+---------------------------------------------------------------------------