61^n=c mod n (2 <= n <= 10^10, 1 <= c <= 100) c | n ---+---------------------------------------------------------------------------- 1 | many 2 | 59, 2629, 172013, 1249229, 3061589399 3 | 22, 26, 29, 242, 749, 1547, 3478, 11882, 19058, 41162, 217807, 3616582, 9497611, 147245407 4 | 19, 63627, 226977, 389001, 13846683 5 | 7, 259, 836, 1858, 1746062, 4800998, 5380963, 13845836, 57244621, 95100469, 312275719, 1388615756 6 | 11, 85, 5165, 48095, 817445, 6950855, 208173481, 5090971045 7 | 33, 57, 543, 1238, 160122, 175593, 580873, 821199, 964911, 1930542, 2389782, 7811682, 16907511, 52605634, 73172966, 114838527, 248642949, 495822209, 729546747, 952834854 8 | 53, 240224333, 4421089019 9 | 13, 28, 44, 52, 58, 76, 154, 247, 296, 364, 374, 484, 1144, 1498, 2494, 2632, 3094, 3496, 4808, 6916, 6956, 8302, 11704, 23764, 24856, 37336, 38116, 44044, 50596, 54796, 82324, 83707, 92152, 95708, 146188, 171094, 210184, 256234, 275044, 280088, 289066, 348964, 374374, 435614, 501128, 539644, 614174, 748424, 993928, 1607818, 1847576, 2448754, 2511028, 2593942, 5573512, 6255802, 7233164, 18995222, 26403844, 27878008, 33922543, 34622104, 40053748, 50035258, 54341224, 68084104, 78638248, 94425592, 94481464, 107358121, 219478534, 260831848, 294490814, 337358164, 393797404, 429861014, 456971242, 612043894, 617070454, 843139654, 1130674168, 1177231939, 1536350794, 2212604056, 2686934294, 2874292564, 3232971562, 3239775994, 3449878348, 4172645554, 6009737962, 7827220492 ---+---------------------------------------------------------------------------- 10 | 17, 413, 2407, 9809, 30779, 47033, 75657, 972261, 2373447, 9846729, 184776689, 775911841, 3338659089 11 | 14, 106, 145, 9197, 11810, 41342, 299773, 702490, 14562005, 50180690, 117714973, 1635733930, 8598215110 12 | 59203, 376159, 702019, 1520191, 43078147, 699738907, 1909120927, 6131856703 13 | 21, 138, 172, 204, 206, 579, 1284, 107332, 239466, 350652, 353908, 691356, 827628, 1079746, 15924444, 42230652, 48696006, 193178617, 271418871, 581912247 14 | 47 15 | 23, 34, 218, 339803 16 | 65, 895, 1235, 1905, 2505, 3435, 45393, 120985, 13015155, 118622543, 137581715, 169627259 17 | 188, 926, 1832, 3857, 18412, 25232, 54238, 114958, 1231679, 3027226, 4103536, 17167312, 77976344, 90883888, 106481111, 742929509 18 | 43, 67871879, 100318909, 370595093, 1078056013 19 | 49, 343, 1234, 1401, 3378, 5247, 45594, 99591, 345159, 1915837, 5823238, 19919134, 30503478, 72020597, 73205631, 226748618, 274393647, 1186701649, 3578578722, 6923633017 ---+---------------------------------------------------------------------------- 20 | 41, 989, 7131077 21 | 55, 68, 74, 340, 590, 772, 844, 2180, 5965, 8045, 8066, 78460, 246530, 2604740, 4361555, 4485620, 10925060, 19218677, 28242644, 32302906, 32771254, 77143715, 223484020, 272952994, 645903311, 658696070, 1120710242, 2520636991, 2574348715, 2591390090, 3797386193, 4331538979, 4367850685, 5268692516 22 | 169, 2041, 26533, 226959, 6507227, 7030231, 28852519, 558811513 23 | 86, 574, 37618, 685877, 23451746, 35923694, 55474258, 1064281193, 3314539018 24 | 37, 329, 197477, 19529893 25 | 56, 92, 132, 246, 518, 564, 708, 996, 1038, 1672, 2424, 3716, 7172, 8249, 35992, 46088, 56739, 72024, 75992, 93254, 201956, 226986, 274348, 322872, 324044, 350754, 620404, 840174, 1594024, 1949234, 2152094, 2351762, 2579708, 2637304, 2765202, 3266958, 3492124, 4111669, 4945052, 5886626, 6547358, 7230776, 9601996, 10761926, 11245944, 12952814, 26413932, 27691672, 36042472, 56021882, 57920056, 58151532, 67991262, 78365076, 79031798, 89059566, 96271018, 114489242, 190200938, 215497736, 227565524, 238152732, 238290197, 344046142, 365765982, 428291202, 471241484, 624551438, 707353496, 995762046, 1160433068, 1245585417, 1380605198, 1487477662, 1721908168, 1823704796, 1938885326, 2777231512, 3107678252, 3252465156, 4706723832, 4765549132, 5557324062, 8922981126 26 | 175, 1775, 3115, 19115, 44185, 126025, 151175, 256585, 1114351, 3948343, 12876025, 181362265, 894217975 27 | 3694, 15026, 105629, 1210394, 20093326, 6427073467 28 | 453, 501, 175351, 332067, 660753, 43498083, 71301771, 131854669, 556106769, 1303306843 29 | 142, 143, 20383, 43082, 4696607, 13845812, 114663583 ---+---------------------------------------------------------------------------- 30 | 31, 387474497, 971359981, 1413728107, 2074811503, 3942655733, 3962606527 31 | 35, 51, 82, 245, 267, 955, 2345, 2891, 5763, 9890, 10398, 24941, 35095, 49330, 136310, 159105, 253290, 1118030, 2279955, 5945802, 10998995, 11465657, 88789238, 111239745, 513675962, 601643651, 892442495, 1328669751, 3233063235 32 | (none under 10^10) 33 | 136, 922, 5032, 30751, 347752, 575953, 727217, 805192, 3461452, 5249521, 7002616, 32048956, 1444160288 34 | 303, 321, 1113, 58821, 21185997 35 | 38, 194, 209, 949, 12998, 33319, 39479, 78473, 8150522, 22451953, 40719242, 71701706, 124317722, 164723654, 327923147, 5870968282 36 | 95, 1735, 128105 37 | 198, 207, 591, 614, 747, 6462, 6978, 10318, 12628, 34956, 49716, 116838, 120868, 361878, 659324, 820362, 1169388, 2901998, 6678684, 22108156, 152149228, 381324108, 458483659, 1173345476, 1796306028, 5811246934, 6572698308, 6840096223, 8340944038, 9251824572 38 | 5125361 39 | 526, 9911, 3089786, 3668896289 ---+---------------------------------------------------------------------------- 40 | 69, 363, 28193, 45903, 438603, 754009, 971373, 9529113, 23325657, 73031289, 84837973, 848190363 41 | 46, 370, 428, 730, 2588, 3890, 8585, 19496, 22340, 27010, 28382, 57320, 336860, 3923380, 8300360, 23083922, 23134486, 192114049, 211149065, 1327055848, 2576699276, 2991103606, 5304130430 42 | 579679, 1625243, 80178667, 1965824629 43 | 102, 327, 1041, 1226, 2226, 9618, 16842, 505298, 784529, 56569517, 239376554, 432944322, 1461677053, 3445654002, 9297302471 44 | 1448431091 45 | 1838, 2681, 3524, 15716, 803398, 28865324, 198592861, 276886858, 2546861597, 7472758418 46 | 99, 123, 255, 981, 3785, 11805, 371905, 588015, 702477, 3607965, 4813839, 11536715, 120971439, 567581643, 763609419, 1011605319 47 | 334, 4726057, 285609878 48 | 15613, 5940259, 24475867 49 | 66, 114, 176, 456, 464, 752, 872, 932, 1072, 1086, 1276, 2476, 3368, 3372, 5352, 7844, 12644, 20634, 20688, 20764, 20976, 26448, 32888, 56456, 56496, 56733, 71763, 73986, 91428, 174192, 212208, 320244, 340482, 351186, 462832, 498012, 777991, 867714, 908792, 1161746, 1345488, 1642398, 1929822, 2627888, 3239538, 3239952, 3861084, 3982956, 4604176, 4730632, 4779564, 5871426, 6515128, 7062928, 8068236, 8132532, 10528744, 12966064, 15623364, 16734174, 26647402, 27381318, 31044848, 33815022, 38836446, 42442136, 44973016, 52586396, 59099784, 60621247, 64163076, 68754948, 70110122, 105211268, 108720546, 112368272, 113240048, 146345932, 173835176, 229677054, 250932824, 254129768, 263660052, 330758768, 345224836, 402557712, 450486384, 497285898, 546062497, 660742448, 732223554, 843137133, 991644418, 1153046588, 1459093494, 1641976226, 1905669708, 1935063748, 2009492592, 2583916016, 2799973608, 2988331818, 3231294603, 4368776872, 5884108432, 5911172076, 9060244962 ---+---------------------------------------------------------------------------- 50 | 180107, 2439331, 3521571581 51 | 70, 734, 1450, 3545, 4765, 13961, 21050, 148745, 610450, 2516705, 11562269, 13871950, 1081435987, 4085354434, 5064561838 52 | 77, 201, 3387, 5747, 271649, 3682049, 8047173937 53 | 262, 19694, 20567, 114428, 464657, 513434, 1011722, 21364397, 59503244, 66271852, 132119276, 272518004, 543486986, 1974619724 54 | 25284953, 411046049 55 | 63, 94, 189, 2526, 3114, 3798, 5286, 5403, 19269, 46302, 66213, 70269, 837941, 1064034, 5665113, 67639442, 121534759, 187368718, 317601986, 322115022, 964433169, 1078257597, 1383607667, 1395237077, 1956633213, 2702458854, 6782590602, 8075321766 56 | 391, 171751, 9384863, 61013647, 536772307, 776500979, 844596245 57 | 458, 629, 6922892, 18922504, 19079596, 38506406, 81049448, 2114967676, 2358755876, 3519022664, 4199786456, 5236072981 58 | 226923, 303789, 7959961, 9395189, 210837819 59 | 623, 1739, 3662, 3938, 5805538, 615541669 ---+---------------------------------------------------------------------------- 60 | 135547 61 | any prime 62 | 23542093, 184107473 63 | 118, 1727, 2167, 8213, 1960831, 2073151, 74311774, 99997594, 1189724014 64 | 3981, 21933, 190881, 680931, 1167003, 16549217, 41540049, 63423819, 77746101, 89578053, 651078471, 915633297, 2560759767, 6067622271 65 | 112, 232, 448, 724, 914, 1162, 1264, 1856, 2732, 5216, 20272, 30016, 31712, 39632, 40792, 50144, 205912, 216341, 339556, 619024, 827984, 850208, 1732904, 2269792, 7116256, 8854672, 12328016, 18607016, 65574112, 97341916, 202380472, 324112424, 1061685184, 2271263296 66 | 497, 6755, 208781, 296077, 343259, 1263731, 29516051, 61076317, 120656605, 7399626605, 7867781327 67 | 98, 177, 1923, 22818, 41258, 13547298, 38721162, 80915046, 1294708791, 1543395037, 8368632849 68 | 611, 85897, 59453449, 152116991, 566584849, 1442708447, 5284323319 69 | 166, 1588, 34876, 493042, 16247354, 151818502, 5188607356 ---+---------------------------------------------------------------------------- 70 | 129, 5277, 581991, 892606699, 7058624367 71 | 146, 815530, 6013010, 37846135, 214893214, 422298115 72 | 1991, 14317, 220891, 2409360871 73 | 119, 184, 548, 573, 666, 1788, 3204, 4142, 4319, 4668, 9864, 16844, 46843, 66091, 90419, 528119, 616712, 1540551, 1902216, 2482148, 2610134, 3951144, 4496312, 13325436, 21099682, 94715128, 427480077, 573562424, 1587209436, 2146682262, 2610128763, 9849161754 74 | 2743, 25597, 31037, 2501941, 23941417, 31971823, 218710277 75 | 3646, 25721, 1167098, 4991539, 5462737, 5482099, 18790846, 77619742, 134500889, 3775849481 76 | 105, 115, 165, 185, 275, 525, 825, 1095, 1155, 1335, 2005, 2175, 5775, 6483, 6845, 54175, 69135, 118965, 134479, 411225, 421575, 443715, 750075, 1223103, 1292225, 1421551, 1662675, 1781997, 6614025, 7122445, 9409443, 11720195, 14440965, 72424275, 153526505, 162824225, 207559605, 288035895, 337729215, 6663318333 77 | 292, 1822, 189668, 289372, 34451338 78 | (none under 10^10) 79 | 429, 897, 1214, 6202, 8727, 39234, 4067239, 6723366, 6805849, 9419581, 9706398, 62701381, 120030963, 369978942, 491700702, 641130326, 819082797, 936745917, 937503363, 3963105714, 4046141386 ---+---------------------------------------------------------------------------- 80 | 161, 364511, 788459, 148896569, 1519885199, 2249185847, 6807396913, 9243384941 81 | 88, 104, 116, 140, 152, 182, 260, 308, 410, 476, 494, 560, 592, 728, 748, 920, 940, 968, 1030, 1040, 1090, 1492, 1520, 1820, 2120, 2155, 2288, 2870, 2996, 4598, 4940, 4988, 5264, 5282, 5330, 6146, 6188, 6992, 7280, 7748, 8888, 9616, 12260, 13832, 13912, 16604, 17630, 17908, 22040, 23408, 37310, 37685, 39578, 44720, 46840, 47528, 49712, 53840, 54530, 62740, 66512, 74672, 76232, 88088, 101192, 105370, 105686, 109592, 126140, 138320, 164648, 167216, 167414, 184304, 188990, 191416, 234962, 255920, 292376, 301454, 335270, 336830, 342188, 396188, 418418, 420368, 423980, 512468, 538655, 550088, 560176, 578132, 637520, 697928, 748748, 751058, 871228, 1002256, 1016740, 1079288, 1153880, 1202936, 1228348, 1352330, 1358588, 1364336, 1456220, 1496848, 1584380, 1722260, 1974740, 1987856, 2008370, 2008760, 2215336, 2506760, 2578268, 2665040, 3215636, 3587612, 3695152, 3775792, 3806060, 3943004, 4440080, 4710518, 4897508, 5022056, 5187884, 5465720, 6336980, 7129136, 8187290, 11147024, 11626160, 12275240, 12511604, 13098488, 14466328, 14558699, 15034948, 17020058, 17506790, 17879480, 20499910, 21301520, 22187920, 23184140, 26412848, 26523728, 27891890, 29092888, 30478448, 31093220, 31763060, 34668620, 36562040, 37990444, 38832392, 45096820, 46819268, 49512008, 52807688, 54223598, 55756016, 64726448, 66917552, 67845086, 69244208, 71069180, 72002860, 75463388, 77692360, 80107496, 86592830, 91848698, 97740698, 98844980, 100070516, 108682448, 108801290, 110462576, 112803728, 118721960, 125868020, 126028136, 126121580, 128227190, 133551088, 136168208, 140087948, 140963660, 141767116, 152596340, 153089612, 157276496, 188851184, 188962928, 196792838, 202847740, 210628028, 214716242, 224395640, 250620188, 253711952, 274125340, 286770698, 310417160, 343171160, 350709788, 377982920, 414702320, 438957068, 453025160, 465150584, 469751882, 521663696, 542543644, 580177040, 588981628, 674716328, 719758988, 754795496, 763271990, 787594808, 824443820, 859722028, 870040090, 913942484, 914142380, 1063115080, 1161706238, 1224087788, 1234140908, 1297663598, 1335780410, 1379151536, 1437353918, 1563507530, 1623456758, 1686279308, 1847101390, 1980684920, 1996675982, 2261348336, 2281524560, 2354463878, 2576673974, 2730939508, 2850224912, 2855667860, 3008720560, 3030050384, 3072701588, 3181251320, 3258449780, 3300158222, 3556028840, 4076159630, 4327115792, 4425208112, 4460742416, 4624623290, 4853458588, 5230549520, 5295221036, 5329437890, 5373868588, 5486279956, 5748585128, 6134214320, 6465943124, 6479551988, 6559108028, 6646514060, 6744359248, 6899756696, 7348099970, 7350140720, 7733654576, 8345291108, 8628912890, 9349082810, 9469990418, 9619023440, 9997378040 82 | 133, 1939, 3043, 3753, 4449, 14061, 65823, 278073, 1058283, 11030661, 43640937, 871995321 83 | 214, 24431, 69094, 83831, 427346, 436594, 2306614, 41476258 84 | 583, 159587, 4123823, 31689269, 33025379, 57819491, 3454815211 85 | 87, 202, 222, 489, 894, 1554, 7476, 13692, 83364, 242908, 514374, 667518, 2033751, 5433492, 19218287, 23758518, 61780666, 62409396, 92415786, 140884332, 316452948, 329285269, 776962236, 2448794316, 2496207417, 3127569898 86 | 61385, 68795, 63378265, 746829415 87 | 158, 442, 4699, 165763, 178058, 4222154, 9115171, 10135679, 260686933 88 | 159, 2967, 4281, 4773, 199821, 356943, 677751, 33288907 89 | 454, 584, 1048, 3013, 28558, 407228, 411329, 607177, 781796, 943688, 974533, 1584919, 2235908, 3046436, 3595688, 4447211, 28043231, 143454392, 168687128, 340270987, 1633321988, 2802275051, 9103518728 ---+---------------------------------------------------------------------------- 90 | 840599 91 | 174, 295, 402, 615, 1590, 2130, 2502, 2610, 2763, 7563, 8790, 13983, 108482, 140345, 508455, 566415, 589242, 2575470, 2764222, 3242490, 4775094, 6409290, 9196630, 11384410, 22720746, 29724795, 64481981, 81137894, 87235831, 167444222, 175172990, 320816502, 574223670, 1191016665, 1361509755, 4539374145, 5866936182 92 | 1643, 6059, 439679, 2261102521 93 | 238, 506, 956, 1814, 8276, 45386, 105226, 1943326, 2424362, 192527822, 289881689, 349722406, 1112896906, 2922626557, 5018913754, 9667866596 94 | 121, 1001, 27291, 44891, 192401, 226887, 234861, 471911, 774521, 1005631, 744348561 95 | 938354, 6065879, 25707662, 382935422 96 | 407, 445, 511, 47005, 799309, 1429687, 9489845, 48203035, 289074205, 856722145, 1284928033, 7243839799 97 | 111, 147, 219, 264, 302, 1356, 1424, 5214, 5439, 8103, 9093, 10731, 12126, 13792, 20271, 21083, 23344, 33999, 34964, 79158, 98528, 107967, 127074, 397047, 608154, 851664, 2402801, 3367264, 10093532, 13321248, 17987244, 23410684, 27247461, 40794774, 45320079, 51030348, 79266912, 112463384, 245853344, 296614689, 1007417019, 1203890424, 2244775648, 6134914592 98 | 4747, 1411687, 3297347, 1864643857, 4115947757 99 | 361, 3622, 11174, 1685126, 2975419, 21530921, 586942471 100 | 657, 8403, 58923, 10482651, 14653501, 41783821, 103443209, 120683769, 2001417189, 2607121197, 4550259141 ----+---------------------------------------------------------------------------