31^n=c mod n (2 <= n <= 10^10, 1 <= c <= 100) c | n ---+---------------------------------------------------------------------------- 1 | many 2 | 29, 37612843 3 | 7, 958, 185173, 19549178, 461808358, 3248067401, 6878153527 4 | 29787, 382729629, 1274449847 5 | 13, 44, 221, 478, 556, 604, 13307, 14429, 51611, 112244, 168649, 520564, 2310044, 24061564, 50654471, 1548032299, 4018696922, 4109225393 6 | 113413, 156301, 253795, 511895, 10511815, 17426615, 28629145, 152409293, 3388750627 7 | 51, 106, 219, 48982, 34651774, 92125447, 762781486, 887503674, 6209057158, 6621582914 8 | 23, 1007, 1121, 23921, 29263, 4705739, 2342882039, 5684367247 9 | 11, 14, 34, 56, 121, 964, 1916, 2216, 5014, 6356, 6776, 13336, 34444, 263864, 307076, 370346, 1111582, 7279976, 22140782, 23042818, 26644184, 26718956, 28120538, 33319124, 39098356, 82226548, 134794726, 145333496, 200994964, 204077572, 271233116, 391526666, 412914436, 634633534, 792068644, 802296104, 923616716, 1274835166, 1353556996, 4384401131, 5399336648, 6496134802, 7476283556, 9661789844 ---+---------------------------------------------------------------------------- 10 | 3309, 4897, 24411, 100449, 172537, 694099, 2368763, 5163363, 37859739, 50140619, 238969317, 262624203, 2368929501, 9170871367 11 | 38, 70, 365, 10630, 76510, 94318, 98045, 159730, 2031746, 2785514, 6896030, 235846970, 350486626, 1252561265 12 | 19, 161, 203, 7679, 13853, 4623269, 509114101 13 | 21, 68, 138, 158, 1236, 2012, 2127, 4692, 766884, 928491, 8632969, 19293558, 21887742, 52080441, 90675348, 180501252, 232899782, 375931841, 1592877733 14 | 17, 3223, 64457, 126299, 9907061 15 | 22, 86, 2882, 2384917046 16 | 115, 695, 995, 1191, 12367, 14441205, 16213565, 112847689, 264628615 17 | 118, 23048, 26512, 230876, 650344, 1184306, 1844912, 5245784, 5943511, 17422129, 82833499, 3850440332 18 | 37237 19 | 261, 314, 477, 2481, 2686, 3609, 14646, 19638, 40398, 162113, 692993, 955502, 7758317, 10724499, 69643049, 162994563, 316927854, 406554858, 687017382, 1164148681 ---+---------------------------------------------------------------------------- 20 | 60212617, 1107362201 21 | 94, 305, 7060, 7388, 121355, 234665, 434110, 38841023, 107491612, 210629315, 242123780, 2795679580, 4453762574, 9440329490 22 | 29769, 427353, 970223, 1234257, 132543573, 1133722671, 1490805957 23 | 134, 2786, 2340977, 3218863, 7261058, 172836823, 3540514286, 5132381026 24 | (none under 10^10) 25 | 26, 28, 33, 78, 88, 92, 123, 318, 442, 598, 858, 956, 1112, 1146, 1208, 1353, 1524, 1686, 1763, 3576, 3706, 3976, 4008, 4596, 15308, 26614, 28626, 28858, 33528, 36492, 40348, 77962, 78023, 84583, 94822, 103222, 145012, 224488, 230282, 242536, 337298, 374584, 410456, 465582, 597903, 612348, 719156, 775294, 876363, 1019914, 1041128, 1577498, 3148508, 3394846, 4565418, 4566428, 4613158, 4620088, 6033118, 10977546, 14477764, 18395608, 18719974, 19035368, 19095014, 22802316, 25403586, 30554788, 37652564, 38559036, 42182796, 48123128, 56578188, 84870698, 87127482, 101308412, 101308942, 103190442, 108155058, 117556122, 118061356, 130044804, 137563964, 140055828, 149841978, 178435464, 182144536, 191017398, 264384978, 274342306, 400734646, 1014737646, 1122402936, 1722965398, 1830701522, 2163285606, 2200147244, 2662511028, 3096064598, 3155217853, 5069786826, 6399249373, 7308703662, 7625142174, 7751607304, 8037393844, 8218450786, 8865804178, 9771138078 26 | 35, 77, 1175, 4025, 5275, 66475, 163595, 1335865, 2419907, 30616487, 122370275, 146449925, 1094683825, 4725676313 27 | 209, 437, 934, 10219, 740069, 6557107, 9819029, 32176709 28 | 549, 9921, 1078463, 1296189, 1409649, 34809237, 122755959 29 | 466, 923492, 33326941, 153140357, 798924481, 1598463164, 1793796091 ---+---------------------------------------------------------------------------- 30 | 1558391 31 | any prime 32 | 5033228393 33 | 58, 136, 371, 9832, 22712, 31367, 47192, 115436, 405461, 3101216, 4252312, 10205464, 14452384, 52845934, 59452072, 312506032, 352665784, 1275725138, 6257073803 34 | 39, 327, 8043, 37947, 43563, 137319, 3797859, 42694593, 235764543, 275439251, 453731439 35 | 926, 209247578, 311917789, 1522350734, 2303853661, 5033374441, 5836139282 36 | 565, 2563, 129785, 253355, 3689571169 37 | 57, 87, 132, 153, 164, 171, 627, 909, 969, 3322, 4959, 6127, 7508, 14193, 24363, 31977, 63198, 140052, 149697, 227887, 385737, 521037, 601521, 631988, 675092, 841484, 1235772, 1587798, 2585241, 2620772, 4898102, 8137139, 11869167, 18619449, 22631337, 44201034, 71204598, 84644884, 147917274, 532753287, 1006567161, 1895836437, 2268970101, 2651000517, 3494226804, 4449249396, 7342567452 38 | 1561, 351697, 14603479, 18496489, 30254639, 99606241 39 | 922, 8174, 181373, 32464427, 53176339, 108936358, 604605358 ---+---------------------------------------------------------------------------- 40 | 119, 141, 633, 8823, 598791, 443590429, 1258747049, 6623940511 41 | 46, 235, 1460, 2168, 5560, 5944, 6035, 14780, 37390, 91880, 92348, 169432, 171580, 304565, 1303864, 1956730, 3387385, 9318440, 26869510, 158039785, 218379020, 418701890, 1064520290, 1146483640, 5849268730, 7684810486 42 | 2512157, 27397759 43 | 111, 201, 35187, 72786, 478506, 17092483, 126786234, 361814146, 1538451346, 2114010046, 6197727187, 9803748386 44 | 949, 879503, 1069637, 48617467, 87798773 45 | 76, 116, 458, 1676, 4879, 104629, 554458, 144864164 46 | 85, 95, 1555, 1983, 4905, 7005, 16677, 425969055, 721836285, 4196888415 47 | 143, 253, 914, 1169, 8567, 371503, 705887, 3105938, 738129431 48 | 1649, 1716527 49 | 102, 152, 212, 264, 282, 374, 438, 536, 696, 1748, 1808, 1902, 3344, 8816, 13784, 13904, 14871, 24636, 64808, 65656, 97394, 97964, 98603, 151334, 178478, 187536, 267544, 289392, 294158, 434288, 556144, 648444, 770678, 1082344, 1167254, 1270796, 1324292, 1401396, 1913682, 2246352, 5396424, 11706924, 12256422, 15209976, 15390192, 15698636, 16954143, 19017448, 19261924, 19564176, 21534524, 23759171, 30447728, 46740254, 54017634, 63659912, 69303548, 86344536, 94618064, 116590722, 130218248, 134983976, 136109192, 139490772, 148828492, 160297448, 182260254, 184036508, 184250894, 217666668, 228750728, 245104142, 251076804, 267104571, 359786198, 382390192, 408659568, 531555888, 566624784, 633026202, 813786874, 843378664, 853913976, 982616198, 1312065668, 1525562972, 1598886062, 1775007348, 2095827802, 2136277502, 2193135888, 2603522536, 2706254254, 2808169584, 3338238521, 4254312292, 6037623336, 9207386966, 9587226302, 9678059238 ---+---------------------------------------------------------------------------- 50 | 1501, 149509, 1230193, 4918777 51 | 130, 182, 335, 350, 650, 754, 1066, 4550, 21365, 27650, 43706, 45710, 52726, 147325, 750230, 1334065, 3144050, 8547670, 14649650, 39570986, 123293210, 147799675, 376947410, 518066990, 752352818, 1435390502, 2737760774 52 | 69, 1293, 23077, 37513, 598627, 2390521, 791542099, 822925291 53 | 172, 236, 238, 364, 454, 13924, 40876, 61852, 831524, 5908292, 30422602, 87450121, 1183564564, 1625368108, 1698202324, 2529926708, 9627067559 54 | (none under 10^10) 55 | 63, 177, 189, 207, 302, 846, 2406, 10899, 25893, 38001, 51849, 72387, 87507, 109893, 253197, 737742, 934563, 1065301, 1906569, 1985562, 3129903, 3374637, 4476573, 15254757, 40583538, 49532094, 691916463, 1631857269, 3069337086, 6842552319 56 | 4343, 61745, 319385, 690635, 2602645, 148921685, 6140994035 57 | 226, 328, 344, 356, 5188, 6584, 20008, 27388, 587816, 622298, 1065508, 4075256, 38531308, 94462552, 175842092, 1310179228, 1789463842, 4181125934, 7076644648 58 | 159, 24467, 19090313, 55767939, 68595731, 139921217, 1681094391 59 | 82, 511, 902, 3997, 5429, 15001, 3796123, 6423142, 48554554, 75472282, 142382042, 392994202, 2158326487 ---+---------------------------------------------------------------------------- 60 | 841, 153907, 1099631, 4297891 61 | 145, 618, 2140, 2973, 4980, 7835, 12405, 61564, 67156, 153345, 567285, 832940, 861654, 1090972, 1861055, 3640445, 3675090, 20250335, 46396780, 91753445, 196088460, 269939495, 565244430, 960937314, 2802177371 62 | 527, 7199, 14167, 22873, 549599, 1581887, 13233791, 1072107007, 9664894249 63 | 898, 264197, 45112922, 1196371238, 6677381138 64 | 981, 1101, 6281, 9717, 77499, 89361, 590687, 4830723, 9625431, 10264227, 24429987, 510913371, 714748227, 777688913, 930329991, 1148188887, 2489767209, 3634193961, 3823349541, 5251842639 65 | 188, 224, 289, 1228, 1304, 15008, 16712, 35504, 36512, 44728, 212552, 247232, 437984, 1899968, 1955792, 2663708, 5951456, 11950496, 18935744, 24121832, 27718802, 48914381, 51474272, 70025338, 86789024, 97878746, 127066688, 166819252, 250698731, 920677663, 1347670352, 1377117446, 2068149563, 3015461792, 4053255584, 5552092484 66 | 2443, 2863, 5845, 9553, 10265, 13945, 284255, 3960313, 33711547, 64210067, 67024297, 1553204903 67 | 298, 3514, 7431, 53358, 99798, 171201, 705918, 26419499, 1137361462, 1541739777, 4321194106, 8238595647 68 | 4067, 35567, 660863, 778463, 3847297, 6479921, 16748123, 37089227, 53973269, 66120679, 104540177, 188264621, 1054184873 69 | 361, 446, 1957, 9988, 22033, 50179, 99458, 165227, 573628, 923452, 117515852, 194498497, 2454625804 ---+---------------------------------------------------------------------------- 70 | 169, 5577, 29289, 29721, 42757, 66417, 333377, 1292577, 2393247, 4664517, 75295077, 84614881, 707177757 71 | 178, 8857, 98003, 137966, 751330, 2657113, 3578635, 41751935, 388318570 72 | 3013, 24931, 611243, 11332649, 44356027, 2732714293 73 | 74, 91, 184, 222, 381, 436, 666, 1068, 1412, 1702, 1703, 3409, 5499, 6769, 13236, 69354, 82946, 136872, 274183, 359298, 422022, 666294, 726458, 1898766, 2142648, 2711997, 3528111, 43871103, 65135614, 122793228, 151234977, 225924618, 366266766, 537423464, 1119272184, 1261451434, 1823613894, 2392517606, 4959180522, 8242383997 74 | 6731 75 | 886, 212541814 76 | 105, 445, 525, 849, 3759, 16455, 21445, 30795, 38451, 111885, 676725, 1004015, 1874775, 6495531, 7542885, 19552575, 65605411, 71197565, 3809304935, 4781063175, 7981989915 77 | 16468, 21794, 31858, 110078, 630526, 923444, 28488226, 2550764341 78 | 1132585067 79 | 98, 602, 834, 1857, 4214, 4607, 29413, 163142, 2589398, 4542398, 6384918, 8578047, 9438758, 20321799, 29863442, 78575071, 665739033 ---+---------------------------------------------------------------------------- 80 | 259, 583, 1717, 1897, 387893, 9221317, 33064067, 59992391, 853789763, 6632669029 81 | 112, 205, 242, 280, 340, 388, 430, 580, 590, 920, 1414, 1780, 1928, 3832, 4432, 4630, 4715, 5860, 7190, 10028, 10520, 11920, 12712, 13552, 15572, 17330, 19256, 23690, 26672, 28495, 32980, 46480, 46864, 56024, 58820, 59920, 68888, 101560, 102160, 107002, 122290, 128720, 144232, 173320, 183080, 185080, 202037, 257240, 281465, 349135, 356380, 446008, 507892, 522859, 527728, 531664, 537520, 614152, 662932, 677680, 738824, 740692, 1511860, 1529720, 2075540, 2076964, 2223164, 2254840, 2311444, 3571760, 4864564, 4936060, 5002480, 5693170, 5700820, 6557480, 7791802, 8009680, 8719960, 8910280, 9391540, 10003220, 11015120, 14559952, 15169840, 17461642, 17639420, 18056680, 28550980, 31064572, 35728580, 36173620, 41455120, 41809648, 44281564, 46085636, 53288368, 53437912, 56241076, 59341492, 62618620, 66638248, 72055804, 72059830, 74503576, 76999510, 78196712, 95340742, 110031140, 114387280, 122809040, 142470320, 150367420, 164453096, 177623140, 179900980, 202377532, 205678640, 205693936, 217986985, 237154192, 269589452, 286291540, 290666992, 303117808, 328133848, 333835096, 342765220, 386954612, 401989928, 408155144, 408946180, 449519888, 452978840, 531915380, 542466232, 551186180, 567342760, 783053332, 802760020, 825828872, 951116048, 965687380, 1031536784, 1035865732, 1207900112, 1269267068, 1360428980, 1477065520, 1567012870, 1584137288, 1604592208, 1742200760, 1847233432, 1863806122, 1887730060, 1945443082, 2146173608, 2416841140, 2521506224, 2549670332, 2707113992, 2743047160, 2792170832, 2862314396, 2868889360, 3082942852, 3154437652, 3259946468, 3357191440, 3697774180, 4677108340, 4799191012, 5388877396, 6446422364, 6622210360, 7008813320, 7464755404, 8768802262, 8909927656, 9438710512, 9729095228 82 | 99, 1377, 9903, 19293, 22137, 46629, 82161, 83511, 431409, 605869, 2239411, 2257617, 2362239, 2781893, 63251091, 292798769 83 | 646, 689, 878, 1462, 124813, 624226, 1579877, 1681849, 14724334, 76123021, 1466689762, 9519411046 84 | 551, 91523, 373559, 863176777, 2653998043 85 | 146, 452, 908, 4668, 4922, 14853, 55524, 59244, 66252, 159132, 222923, 1362732, 2448642, 3331092, 3921564, 10612356, 10715169, 53568716, 63393114, 2333860998, 6783445596, 8643693756 86 | 485, 6227, 101651, 222821, 295145, 965921, 2251537, 5389631, 4310884177 87 | 2414, 3841, 46478, 49513, 1163029 88 | 29703, 67731, 373881, 5387047, 26414457, 364419373, 8741974427 89 | 218, 376, 323612, 461716, 1309912, 79093724, 104161912, 109438259, 465221672 ---+---------------------------------------------------------------------------- 90 | 26123, 713893, 442086173 91 | 198, 710, 870, 1255, 2115, 7898, 9505, 26854, 27990, 591930, 2385755, 4470678, 4721838, 40137385, 59166906, 106373070, 154967922, 492944958, 922764215, 940497795, 1383797943, 1482754878, 2833999170, 4345898523, 5780440759, 7259605798 92 | 215567, 4421051 93 | 124, 434, 986, 1364, 1798, 2708, 8308, 11594, 138818, 222866, 323578, 343574, 454894, 572539, 884492, 1453466, 4185062, 7473914, 14861086, 22621489, 26454439, 109186154, 509433181, 692917187, 1152455194, 2286229106, 3168777964, 7928349044, 9345820759 94 | 1563, 4417, 8607, 36769, 197733, 1031467, 4844623, 182564787, 3759490437, 8953816711 95 | 866, 119323, 1086106, 4381174, 6563339, 8688881 96 | 26255, 314605, 2354105, 7575301, 143312695, 1078946831 97 | 147, 176, 231, 303, 357, 516, 848, 872, 1056, 1659, 2877, 4128, 5464, 5648, 12448, 14916, 24816, 38476, 41056, 58317, 61792, 68384, 83208, 127407, 252987, 307488, 318232, 1614921, 4106096, 4731488, 5042634, 5680608, 5877336, 11051709, 11308368, 12234156, 13383766, 35698902, 49058751, 56986896, 108557216, 123521064, 159235296, 186658544, 329919216, 398933274, 443751927, 707191653, 799791528, 1537141296, 1550311636, 3108462676, 3780703293 98 | (none under 10^10) 99 | 862, 2119, 7943, 10921, 453427, 6300247, 349575571, 594933221, 7019565089 100 | 9897, 39579, 64117, 2060847, 3882933, 115465437 ----+---------------------------------------------------------------------------