7^n=c mod n (2 <= n <= 10^10, 1 <= c <= 100) c | n ---+---------------------------------------------------------------------------- 1 | many 2 | 5, 143, 1133, 2171, 8567, 16805, 208091, 1887043, 517295383 3 | 46, 2227, 6684830083 4 | 339, 340146491, 7641467979 5 | 22, 2396, 65836, 1145458 6 | 387497, 789211, 6226069, 3365314237 7 | any prime 8 | 535 9 | 10, 52, 88, 92, 410, 872, 968, 2491, 4454, 4808, 15170, 27359, 42010, 120130, 176342, 484034, 604762, 1128844, 1440868, 2846008, 3395018, 3570268, 3656536, 3973288, 4021798, 4031092, 5736776, 16796258, 25081604, 86426770, 100479368, 103813798, 109966972, 117593668, 176847409, 244061896, 362045444, 383992648, 448844392, 784179916, 905100149, 1119254968, 1279446718, 1315577098, 1714916428, 1763555398, 1789509748, 2591774090, 3435223508, 4100269370, 5098570244, 6070925516, 7849789730, 8057609510, 9507238844, 9618039944, 9908181124 ---+---------------------------------------------------------------------------- 10 | 111, 153, 657, 32517, 2095881, 594221961, 667906763, 2803232193 11 | 38, 437, 1007, 3525931, 4025734, 15223997, 28402511, 43376237, 87481187, 96982346, 1115731586 12 | 8399, 24511, 1618511, 944434345 13 | 15, 33, 204, 796, 1555, 15315, 58818, 87708, 111396, 451473, 2092548, 3701153, 6125916, 16396015, 27876668, 34774535, 55070286, 87737495, 527010362, 6502175315, 7018491835 14 | 497, 11599, 28489, 70679, 2346337, 168364217, 293903231, 400987097, 997931777, 2045588729 15 | 34, 30206, 58813, 526583282, 7778981741 16 | 327, 150659153, 538242513, 551602437 17 | 365, 596, 1016, 22184, 22696, 34288, 63248, 252521, 390805, 584974, 1969262, 16697348, 27153767, 80729113, 171547445, 217796386 18 | 515, 815, 8675, 41501 19 | 30, 90, 99, 170, 403, 1530, 1629, 5067, 7842, 79327, 248259, 453427, 1138891, 1381662, 1684281, 5538730, 9293594, 11561631, 16839962, 20266770, 21518739, 90143443, 333161858, 421944177, 1433055210, 2760816867, 8622857910 ---+---------------------------------------------------------------------------- 20 | 7219931, 221504611 21 | 28, 68, 140, 340, 413, 6979, 15260, 22372, 127346, 180068, 218212, 224854, 508172, 1301860, 2336540, 2668660, 6096391, 21113974, 23936906, 45482738, 85981028, 166109426, 4852767388, 5739454460 22 | 321, 1865, 258217, 340513, 1644285, 3308883, 3944847, 553473985, 5758020067 23 | 26, 338, 227338, 2162186, 5116982, 12892646, 21035066, 29804893, 1486568401 24 | 223793, 26871077, 119994733 25 | 44, 78, 159, 174, 264, 1326, 3208, 4602, 4792, 7076, 16008, 20562, 20614, 21716, 29356, 83404, 99606, 99822, 131672, 235308, 268554, 282574, 352932, 354776, 471396, 779132, 790316, 904098, 1025134, 1475994, 1659666, 2290916, 2335512, 2727156, 2836164, 2857598, 3554818, 4354188, 5280474, 5811702, 8959938, 13647864, 13968452, 14005956, 16769544, 19470296, 21291582, 21324756, 23213014, 24399048, 25025608, 30737226, 57125406, 81062508, 99629956, 106785156, 127119166, 130640388, 214836204, 311834094, 326970618, 365873684, 406524066, 416725476, 444433278, 916043306, 964066974, 994304454, 1136323266, 1217673372, 1310536497, 1521372184, 1661874468, 2023478418, 2082636222, 2658115338, 2861471758, 3124254346, 3443130834, 3446170248, 7549793016 26 | 10718597, 7155299623 27 | 242, 101882, 434422, 17685602, 1127221418 28 | 35, 63, 77, 135, 161, 189, 217, 235, 297, 315, 357, 455, 801, 923, 1173, 3171, 3423, 3703, 4509, 5797, 7749, 8631, 8883, 9423, 10035, 12195, 17793, 18333, 21591, 23355, 30709, 38279, 41973, 43695, 70767, 71435, 93771, 105921, 109047, 110943, 135933, 166635, 169403, 274515, 275349, 278341, 304997, 373079, 432189, 484389, 781859, 1182741, 1340073, 1570667, 1607067, 1949535, 3204879, 3405717, 4038399, 4043613, 4626261, 4801355, 4834431, 5460721, 6451155, 7142037, 8170029, 8305101, 9734535, 12353115, 12386535, 14061053, 18865847, 19422339, 29025891, 32138715, 36080667, 37166437, 44914149, 49641291, 58102655, 61928837, 71545019, 82641519, 117023949, 131518395, 157699353, 170402589, 182643195, 217691397, 220066273, 253568595, 257098761, 334805429, 501958395, 507781197, 535747395, 557309457, 686838663, 724583559, 741708927, 888737001, 901855989, 917014779, 934779501, 939039843, 998942103, 1362582235, 1541480079, 1660179255, 1858010063, 2276632099, 2866323537, 2928275595, 3017318135, 3229733507, 3378546899, 3400367859, 3651473061, 4414594399, 5522868693, 5584016977, 5911031441, 6763544879, 8165362653, 9804576635, 9987212319 29 | 2330, 2372, 100556, 133930, 264212, 570734, 606170, 609671, 1240481, 19485908, 408524674 ---+---------------------------------------------------------------------------- 30 | 209, 13439, 2042861, 7110526061 31 | 39, 76978, 117618, 1418403414, 3348124098 32 | 305, 5665, 58025, 84025, 1175165, 2210945, 5414539, 80125025, 81219545, 432434645, 608092925 33 | 136, 148, 481, 3013, 4208, 41935, 84776, 312502, 395744, 22609868, 129017624, 225991888, 413250716, 505444829, 604661968, 649269829, 1364303432, 2860226192, 5978079418 34 | 309, 8273305581 35 | 4382, 7031, 109942, 174167, 205877, 275926, 4202459, 326131967 36 | 10596486211 37 | 45, 51, 65, 66, 345, 396, 788, 2021, 2279, 3114, 182451, 300785, 388916, 449454, 1983203, 2531945, 2553994, 3340252, 4035357, 6836394, 15916545, 15953916, 20209038, 123086316, 146279598, 488756963, 569668284, 1238167165, 1656073665, 2542928453, 4613762388, 6218083164, 8462781892 38 | 24751, 2631017, 32565241, 545655833, 2079587795, 3761729695 39 | 7327, 15590, 71690, 157379, 181190, 3583429, 4864183, 6114337, 781594517, 2230503206, 3589411067 ---+---------------------------------------------------------------------------- 40 | 121, 303, 24429, 75003, 42417447, 166281951 41 | 236, 248, 920, 4460, 11209, 37192, 63158, 657059, 1169720, 3454460, 90063860 42 | 78821, 823501, 9730231, 45327365, 59495485, 312729277, 2260141127 43 | 55, 75, 102, 275, 635, 1817, 2895, 6918, 8395, 467835, 562701, 988278, 2851575, 3641475, 37504335, 67368162, 364973674, 584212035, 641766675, 750574275, 1178234275, 3205647975 44 | 4117, 2990023 45 | 76, 124, 247, 589, 16783, 31597, 719918, 13615324, 15368644, 293249629, 785596684 46 | 1751, 11673, 17743, 31113, 4494853, 63854277, 176554729, 268136903 47 | 30514339, 735963194, 1134914294, 2957369567 48 | 83795, 425584051, 851970335 49 | many ---+---------------------------------------------------------------------------- 50 | 1333, 261139, 2011153, 200991853, 944904077, 3159750733 51 | 341, 1111, 11537, 520757, 14225894, 3678908033 52 | 291, 319, 5585, 1164291, 16888985, 24350597, 224012463, 2299047859, 3439136067 53 | 1628, 2348, 5771, 36074, 206998, 937135, 6934274, 10837781, 192596083, 3458423594 54 | 245023103 55 | 282, 834, 873, 963, 32166, 39198, 652846, 739341, 1471182, 7652178, 211058086, 508064877, 6953962578, 9877387098 56 | 329, 17521, 153391, 876113, 8392543, 12999329, 246364799, 991435631, 1260051337, 1987785863, 2886307849, 7018029697 57 | 125, 488, 1172, 2125, 94504, 95764, 115925, 7807144, 121443325, 413760203, 525477998, 538800125, 1552986125, 1930569037, 1996611625, 7259040185 58 | 1649, 6847, 494623, 1015323, 3714771, 3759155, 22978695, 28904529, 40458315, 49390109, 158351521, 678831127, 2801690049, 7723391073 59 | 230, 7379, 80806, 12281530 ---+---------------------------------------------------------------------------- 60 | 2179291487 61 | 141, 246, 1434, 6180, 13740, 14487, 100734, 1981614, 2767740, 25639820, 32428822, 1213990166, 1321935004, 2116778666, 2768257428, 3259206652 62 | 85, 985, 49462463, 293523445, 1977326681 63 | 115, 119, 1211, 1918, 3619, 8383, 20458, 39515, 5068483, 6622679, 11475961, 14999291, 20936069, 36165535, 50031239, 71955655, 82765259, 87038987, 123386935, 177030838, 382003349, 1328372701, 1411562441, 1450527421, 2019628793, 2466663017, 2740273949, 4950533378, 6834835255 64 | 93, 1017, 246291, 357111, 38557773, 873060583, 909659371, 1020439473, 1268582187, 5074134183 65 | 232, 292, 1504, 1856, 12424, 51248, 61111, 216427, 376391, 404918, 1762804, 2706628, 6868016, 21953248, 43593664, 2593890928, 3716698816, 4553106148, 8650940743 66 | (none under 10^10) 67 | 69, 3165, 34417, 117582, 18439942, 62012739, 129715851 68 | 95, 253, 2375, 16967, 19475, 47393, 133715, 294215, 404875, 171797875, 250343753, 7420544975 69 | 130, 212, 10864430, 11694316, 780252166, 1001336834, 1415240551, 2019235748 ---+---------------------------------------------------------------------------- 70 | 507, 3471, 8337, 30499, 77091, 110019, 249519, 2541039, 3668847, 4416727, 11847549, 618728019 71 | 3043, 81202, 121462, 213046, 700394, 297188438, 1730837651 72 | 2977, 66517, 1800409, 2224105, 1625950043 73 | 117, 138, 255, 388, 426, 1656, 2979, 4689, 8616, 10728, 18828, 21444, 143436, 217212, 234216, 236895, 400122, 680376, 846729, 1724808, 1921576, 3986909, 4374915, 39020298, 87311208, 269959815, 275590584, 377358932, 508264355, 519099795, 984310836, 1056714667, 1251024552, 4208122047, 6315857892 74 | 10763, 30221, 41147, 1204909, 1783451, 3239867, 11307743, 18643259, 42423079, 43575373, 1111625033 75 | 289, 5005093, 300543098 76 | 267, 43277, 5816681, 126119669 77 | 332, 917, 3143, 5845, 9485, 93773, 142646, 985558, 1655234, 5446028, 39177961, 43139156, 105748988, 1463069606, 5237291143, 6026315189, 9621958199 78 | 55369, 9186729295, 9727472411 79 | 430, 470, 3090, 8943, 15530, 23514, 766581, 1212117, 1692741, 2176357, 4784818, 9461290, 36110301, 131412657, 186005523, 2034264009, 2250680883 ---+---------------------------------------------------------------------------- 80 | 73487, 2112977, 3444257, 5617391, 77701559, 123836861, 223942667, 2376312887 81 | 104, 116, 176, 184, 260, 820, 848, 1040, 1168, 1196, 1702, 1744, 1928, 1936, 2384, 2920, 3880, 4982, 7160, 8908, 9616, 10076, 19640, 24440, 25288, 27676, 30340, 30920, 36208, 47260, 54718, 64280, 64420, 67460, 70160, 72020, 81680, 84020, 87406, 87740, 110920, 111088, 127664, 143560, 148336, 162352, 240260, 262798, 283240, 309520, 320716, 352684, 381352, 398920, 450320, 454243, 603856, 700669, 835172, 948740, 961220, 968068, 972680, 1101260, 1209524, 1260340, 1382546, 1642792, 2257688, 2372240, 2742646, 2750920, 2881736, 3032668, 3097936, 4160936, 4679672, 5229136, 5692016, 5945264, 6339164, 6790036, 7140536, 7313072, 7585360, 7946576, 7949444, 8043596, 8062184, 8384680, 10479880, 11454248, 11473552, 12187760, 13230032, 13901732, 14661560, 15820376, 16511176, 16828816, 17770220, 20178952, 22337932, 22897040, 26550320, 33592516, 35854096, 40144744, 45899528, 47329160, 48779026, 50163208, 51301480, 52322896, 59435308, 59905040, 78423332, 86007340, 101260016, 103487228, 108786796, 135282440, 146541020, 148474960, 161216560, 162724916, 166657546, 172853540, 187221640, 197010064, 197937340, 200958736, 207627596, 210631864, 210906440, 219933944, 235187336, 271230040, 292462064, 332277616, 353694818, 355151320, 380732728, 394572592, 466637840, 488123792, 579542380, 627117140, 681170360, 697053640, 724090888, 749800916, 767985296, 772492136, 897688784, 930095728, 944845820, 1024929688, 1028705488, 1047748280, 1070443580, 1077186832, 1079693264, 1085018932, 1087135244, 1188255920, 1206331676, 1295607016, 1348299320, 1400660680, 1495213660, 1568359832, 1574300780, 1592996780, 1651417196, 1792563880, 1810200298, 2238509936, 2262054748, 2391320038, 2558893436, 2578453336, 2631154196, 3132197954, 3429832856, 3527110796, 3579019496, 3810942620, 4020623156, 5059451276, 5183548180, 5302318736, 5736335540, 6777336116, 6870447016, 7049853560, 7422707336, 7425783784, 7447169720, 7715014960, 8200538740, 9791740540 82 | 87, 225, 405, 459, 1305, 1719, 2025, 2201, 2817, 4005, 4325, 39063, 146425, 197425, 587025, 642519, 1394325, 2859951, 3460027, 9063225, 36541305, 40551219, 55676385, 267755417, 276735889, 452187459, 584261289, 766118025, 833449473, 1125457785, 4895420247, 5709757425, 9647167329 83 | 517, 851, 2641, 2698, 15751, 208354, 8948449, 17700962, 53273989, 67625218, 67811714, 108715606, 156172894, 358188127, 7518480595 84 | 91, 51821, 63343, 730877, 5075353, 37188151, 164120903, 257966939, 316073681, 504361879, 2600366587 85 | 129, 276, 582, 606, 772, 1419, 98612, 216844, 226369, 391686, 1369929, 1668292, 26165004 86 | (none under 10^10) 87 | 1705, 14459, 687562, 49758986, 886725458, 2204574586 88 | 27715, 3143839, 879147055 89 | 110, 530, 2168, 5170, 11554, 17069, 21272, 101621, 121130, 158677, 264941, 2220130, 8673830, 14332721, 26115401, 38017733, 50076490, 80490808, 127921978, 148194917, 179600038, 1672258244, 3962287388 ---+---------------------------------------------------------------------------- 90 | 33973, 9261509, 11362511, 153957151 91 | 126, 154, 711, 1866, 2814, 8757, 18243, 18918, 68621, 152174, 1629999, 2024134, 2410233, 2894178, 5167662, 5260829, 25209453, 27315918, 88738587, 186834987, 578895711, 698474406, 949999974, 1072174801, 1795827586, 2198205414, 4067428302, 4749518097 92 | 165727, 472145, 24110299 93 | 1012, 1075, 2308, 37195, 53183, 70052, 444835, 1311542, 17134763, 24464996, 33215995, 35190782, 82617959, 567024775, 868807535, 958832275, 9884524652 94 | 249, 6622219, 32782493, 34733949, 40349527, 567568311, 3486954719 95 | 21599321, 247165831 96 | 984586229 97 | 123, 186, 424, 474, 528, 705, 824, 2785, 2976, 5216, 13548, 16288, 19716, 22224, 44183, 45104, 53328, 110256, 123288, 163936, 335136, 356376, 766236, 1205688, 2767605, 3394147, 3830728, 4084816, 8915588, 14576188, 22534908, 27029657, 57366564, 108849289, 138867728, 192502124, 218313104, 220405296, 280427405, 561422424, 770273824, 1383939568, 1885785528, 1895173408, 1904532148, 7672612317, 9430131212 98 | 155, 637, 2695, 6097, 7595, 19915, 23527, 117593, 583247, 4351549, 9057895, 32351515, 75398857, 113727817, 133280455, 191894519, 251944595, 729863935, 1395176695, 1586119759, 2712076255, 3660476435 99 | 2630, 214810, 1070950, 11013619, 2780167717 100 | 1251, 290313, 4211007, 64791271, 401980263 ----+---------------------------------------------------------------------------