89^n=c mod n (2 <= n <= 10^10, 1 <= c <= 100) c | n ---+---------------------------------------------------------------------------- 1 | many 2 | 3, 29, 4089, 704967, 19949753 3 | 43, 74, 214, 2806, 29378, 54299, 846817, 45080777, 391627846 4 | 5, 17, 85, 365, 7633, 264685, 651373, 114342017, 804237157 5 | 7, 39, 1636, 3958, 12207, 13363, 13557, 71509, 153404, 279811, 314521, 397957, 703009, 749302, 1438582, 1672359, 3066061, 12092313, 514608953, 2181866942 6 | 83, 19862267 7 | 41, 2638, 100986, 275629, 1876727, 29527734 8 | 9, 87, 111, 117, 219, 873, 1677, 8103, 12267, 464061, 2114901, 5324533, 24736269, 45908787, 59849259, 96252693, 176072909, 382952061, 401163633, 786254193, 817051989, 1182353769, 1587456027, 2395059693, 4213620333, 9505009197, 9974141999 9 | 28, 46, 86, 104, 148, 428, 824, 1132, 5612, 6118, 7828, 11336, 19432, 32452, 56888, 58756, 72377, 72808, 86494, 108598, 109115, 110428, 113848, 133124, 170312, 272792, 344312, 345992, 1218296, 1693634, 1862345, 2261788, 6460342, 7910824, 12999023, 15880252, 17547934, 19305304, 19759852, 33067112, 33340892, 39482372, 90161554, 104067548, 107697676, 148341752, 153150677, 164068648, 173082884, 258935972, 328396708, 344961832, 349003715, 783255692, 826205906, 3692427586, 3923105116 ---+---------------------------------------------------------------------------- 10 | 79, 2219, 47453, 5120087 11 | 13, 14, 226, 879, 1203, 1946, 2509, 61990, 66530, 72110, 272067, 604771, 1329969, 1874821, 3163670, 11086777, 17978062, 104849270, 140246530, 452747330, 853199678, 856511099, 1613620509, 2592993430 12 | 8407, 799183, 3023053, 8557111, 10495513, 52250443, 939814303, 1680470671 13 | 19, 1318, 3292, 13404, 25412, 40874, 71454, 212678, 393726, 476354, 665839, 703734, 1017958, 1121468, 2972908, 19897469, 20865786, 23130937, 79682916, 106682622, 135222882, 1214428646, 1758566786, 1868588489 14 | 15, 95, 615, 13735, 18905, 20465, 23935, 140991, 329415, 7426481, 72479137, 1251452001 15 | 37, 118, 134, 247, 871, 5893, 97399, 106237, 164933, 715163, 1608458, 562512722, 781757762, 4356409447 16 | 73, 14527 17 | 26, 38, 287, 628, 752, 4484, 29373, 99908, 212186, 616922, 226012989, 3872289919 18 | 71, 7973093, 237133037, 324360083, 1072998221 19 | 49, 343, 878, 1079, 5635, 6265, 46422, 245219, 332874, 757045, 1900729, 7197203, 7882387, 32184191, 89540867, 151892419, 378539455, 928479071, 2792029715, 3334697015, 3611713703, 4281771781, 4587914567 ---+---------------------------------------------------------------------------- 20 | 21, 23, 11141, 100707, 29856579, 79539601 21 | 158, 370, 493, 1412, 1670, 35548, 71417, 491420, 522110, 2962369, 88300868, 227423146, 6360744497, 6932611460 22 | 67, 35832361 23 | 33, 154, 286, 418, 718, 2002, 2782, 2913, 3718, 4246, 6526, 26026, 38038, 48958, 233662, 238966, 644098, 696993, 953134, 2418922, 3708874, 29347307, 30610646, 40308862, 102121723, 116729799, 138449069, 219279742, 783616834, 1444132378, 2124216094 24 | 25, 35, 185, 235, 295, 325, 1555, 40355, 58499, 361831, 382909, 526925, 14595725, 20091701, 55668925, 317618525 25 | 56, 78, 94, 344, 402, 3272, 3956, 5284, 5672, 7772, 7916, 15108, 24414, 26726, 27114, 29372, 31566, 103692, 106674, 143018, 216692, 277256, 280276, 306808, 559622, 594406, 629042, 672236, 720442, 795914, 906456, 1406018, 1498604, 2634888, 2737186, 2877164, 2882534, 3344718, 3771836, 4905137, 5557852, 5931716, 6132122, 6152424, 7787544, 11667256, 12675662, 14120364, 14598246, 24184626, 31915352, 32806164, 33484908, 47570374, 65200434, 88585284, 94902366, 115028652, 140610974, 163072318, 245278056, 283850492, 376176138, 378072572, 382116094, 409981098, 693720484, 1029217906, 1184228652, 1598888648, 1640736786, 2246903544, 2281778137, 2291851704, 2579485362, 2903998676, 3696158152, 4344497596, 4363733884, 5971094686, 6737447064, 7264174444, 8098956764, 9794866614 26 | 27, 2727, 2901, 100143, 914517, 2416251, 46965819, 1061426359 27 | 31, 6541, 7894, 16867 28 | 61, 223183, 568616441, 2403052361, 4496218043 29 | 52, 93, 1137, 3946, 10555, 220435, 251813, 832443, 4826324, 9813548, 1164296013, 3648139466 ---+---------------------------------------------------------------------------- 30 | 59, 391, 1819, 14236463, 15385379, 139916731 31 | 230, 526, 6377, 1057571890, 3355594890, 5222132378 32 | 704937 33 | 34, 58, 248, 1184, 2012, 7796, 8942, 15836, 32992, 288688, 689042, 1857182, 18115231, 62901728, 113322989, 179609632, 660681821, 995018408 34 | 55, 517, 565, 1111, 1639, 1903, 2497, 3047, 15565, 1212655, 2179813, 2844685, 4492405, 23814241, 30695005, 72137791, 171873031, 186859255, 841481185, 1733068205, 2676343135 35 | 7886, 117489, 4258291, 5725271, 9482786, 8274124514 36 | 53 37 | 146, 1228, 3244, 3636, 6282, 371014, 466892, 2366948, 3771294, 62446682, 170252298, 276336756, 346412548, 2587316452, 3269555338 38 | 289, 1037, 46529, 82077, 207213, 253317, 346947, 704931, 1460157, 3351047, 3614261, 160462337, 204266939, 268063491, 7204143737, 8379297501, 8667811981 39 | 434, 1126, 2282, 201866, 723577115, 726143035, 2792029705, 3070836953 ---+---------------------------------------------------------------------------- 40 | 29279, 256249, 742043, 41142791, 258063571, 664271941, 1215824827, 2174268103 41 | 394, 460, 3147, 4514, 5817, 14810, 20307, 33940, 377769, 501476, 964437, 1254844, 4059086, 4169780, 5625039, 117764959, 145840792 42 | 47, 2507676361 43 | 202, 26502, 45266, 84462, 179466, 1220882, 1958014, 486000241, 6492855902, 7866621546 44 | 45, 195, 723, 1515, 2385, 2691, 5655, 21099, 30015, 46995, 135855, 179127, 876915, 1969071, 5209305, 11267955, 12605605, 19596915, 20799987, 56997585, 68939005, 69991935, 1823898555, 2758257105, 5152710933 45 | 77, 116, 143, 253, 358, 2222, 6227, 15481, 35189, 136829, 196684, 364091, 404822, 1544543, 1636537331, 2972958131, 7124465579, 7587300743 46 | 1208597, 23840767, 964295207 47 | 51, 62, 254, 4879, 18057, 20733, 43262, 120998, 669511, 1501702, 12874119, 726513514, 808662511, 8181896947 48 | 5425481 49 | 82, 114, 276, 424, 456, 592, 696, 865, 995, 1336, 1644, 3152, 3964, 4055, 4638, 5276, 5844, 7675, 10536, 12142, 20208, 30025, 41764, 52788, 116476, 158448, 193404, 197072, 201972, 233994, 315888, 439325, 446568, 485796, 500936, 551258, 912228, 1135896, 1183816, 1354776, 1591325, 2052184, 2114886, 2156556, 2272656, 2701938, 3753454, 4083432, 4684612, 5081528, 5222032, 6241232, 7420265, 10020635, 16940244, 22197838, 23519112, 31670988, 33328254, 35020968, 35544886, 39012058, 41586288, 45336436, 45965256, 52354158, 56554825, 59055468, 71358128, 94384844, 97190024, 100730108, 107924944, 246670692, 259154556, 266895917, 318518736, 460139286, 654081954, 727338736, 733509768, 871445242, 987460462, 1140610704, 1246818576, 1503538954, 2830141428, 3319257756, 3365198376, 3532856826, 4758970192, 5206116112, 6377099825, 6594888714, 7491693084, 8234085072, 8613353904 ---+---------------------------------------------------------------------------- 50 | 57, 249, 447 51 | 70, 1574, 4430, 87430, 1096270, 3684730, 13493950, 18664870, 93104150, 607775450, 1062428050, 1488220850, 1524462050, 1658197370, 3237573050, 9472192231 52 | 1673, 1799, 11429351, 129010049, 1578931697 53 | 183, 321, 524, 562, 1179, 1403, 10598, 18573, 38738, 211059, 348921, 478948, 515354, 1415103, 3319893, 5077823, 7206179, 18009676, 99633309, 107535052, 108498362, 119782994, 552558524, 609464367, 815878839, 877368411 54 | 91, 1315, 1651, 24115, 173845, 387907, 892255, 2170987, 21232165, 55899259, 188228467, 225448495, 1303509887, 8286925387 55 | 2538, 6862, 46801, 73614, 1678338, 4500786, 71615718, 86253606, 296594874 56 | 123, 407, 1563, 3263777, 17937119, 439778229, 620171931, 752582743, 917039783, 2568019151 57 | 1966, 23704, 31371092 58 | 1703, 771983, 1517628419 59 | 65, 335, 7862, 15821, 20993, 70491, 152645, 539483, 6661235, 203493405, 222862238, 367185927, 1646687459, 1931256309, 2318694663, 7335294785 ---+---------------------------------------------------------------------------- 60 | 841, 3401, 4853, 26443, 10832831, 74890603 61 | 76, 188, 246, 260, 262, 1572, 1660, 3390, 3670, 4684, 6812, 13988, 26780, 32566, 36942, 54014, 61412, 625132, 666397, 942972, 1016219, 1033861, 5527138, 10517657, 13387292, 16989330, 45741370, 47268660, 49736230, 54428538, 69720132, 70247510, 103513260, 145376202, 242429898, 324452060, 890350932, 1395009958, 1850388398, 2847146990, 8300035740 62 | 63, 201, 501, 1659, 4203, 25011, 922257, 1091457927 63 | 3473, 7858, 222100369, 1396706191, 1430517538, 1440474562, 7242519227 64 | 3995, 906355, 5584059385 65 | 69, 112, 448, 982, 3831, 5792, 11944, 32746, 42176, 83984, 103871, 274112, 330736, 555232, 1120396, 4839104, 8122408, 20315344, 69418696, 116842432, 145041392, 205186252, 713902378, 902994513, 4093423888, 8706761978 66 | 4399, 38507 67 | 98, 102, 374, 1122, 1542, 1738, 1914, 2167, 2618, 3626, 5863, 10846, 18326, 19686, 27146, 34262, 41258, 76886, 96866, 103598, 218078, 229097, 608298, 939554, 1102178, 1196426, 1447754, 1632638, 1771638, 1785542, 1959451, 2077638, 4784174, 5791654, 8422106, 30862622, 64492406, 81159386, 111174289, 317253354, 1001282114, 1003253334, 1067203819, 1203478178, 1462472099, 1806219697, 2050752998, 2096639006, 3159846494, 5996839998, 7659546818, 7743322934 68 | 9457, 21809, 21847, 33549, 704901, 674865121, 6761945327 69 | 302, 1537, 3604, 13565, 15164, 514565, 3381572, 3690716, 10365988, 113838518, 281927029, 1561388084, 1595940086, 4927337732, 6473327815 ---+---------------------------------------------------------------------------- 70 | 80125193, 146333633 71 | 314, 5630, 8630, 52589, 117483, 420423, 426911, 3894791, 10954402, 2087106039, 2994491307 72 | 221, 377, 260021, 2495821, 3608093, 200541809, 1617533021 73 | 152, 218, 666, 828, 1448, 4109, 4626, 19518, 27512, 60344, 255016, 1161892, 12501007, 12731358, 28626236, 31215518, 275991972, 348973848, 734422487, 4130023992, 5291984407, 5573225929, 8073768564 74 | 75, 1115, 1725, 2075, 13355, 14425, 26025, 120325, 140979, 201855, 240285, 966925, 2506425, 598347825 75 | 511, 7846, 48421, 74854, 7789471, 111374806, 263485603, 268769878 76 | 37453, 126509927, 240909497, 302873701, 330395533 77 | 106, 548, 2697, 4307, 10877, 32741, 176223, 310461, 457972, 3585836, 4666957, 7318901, 25552277, 246027772, 345652719, 643623457 78 | 209, 23441 79 | 115, 205, 1655, 2614, 8945, 19885, 23501, 29706, 74495, 89039, 115446, 1887845, 2247005, 21510118, 25902226, 64702246, 100379982, 750785326, 1633903494, 2429922838, 3435664498, 3652918831, 5932417277 ---+---------------------------------------------------------------------------- 80 | 81, 927, 999, 1027, 1863, 3353, 13351, 78321, 90671, 3225771, 7358446899 81 | 92, 140, 172, 208, 244, 266, 296, 520, 560, 580, 820, 856, 1610, 1648, 2264, 2660, 2680, 2740, 2960, 3016, 3760, 7228, 10660, 11224, 11860, 12154, 12236, 15656, 17869, 19664, 20068, 21040, 22672, 25687, 31730, 38864, 39530, 45542, 50120, 57680, 59560, 64904, 108080, 113776, 117512, 144754, 145616, 159440, 164810, 172130, 172988, 175240, 185288, 199514, 214736, 217196, 218230, 220856, 227696, 266248, 277286, 280760, 285310, 293360, 328424, 340624, 358340, 364984, 370310, 429232, 545584, 548360, 549080, 625016, 654860, 688624, 691960, 691984, 720518, 882388, 965236, 1034480, 1191932, 1364680, 1388240, 1526660, 1608008, 1694090, 1853956, 2007752, 2007860, 2121340, 2436592, 2516720, 2590919, 2935310, 3387268, 3410960, 3571034, 3585860, 3724690, 3739568, 3998960, 4129496, 4332464, 4523576, 4668820, 4703024, 4852904, 5072236, 5371940, 5690846, 5934356, 6114884, 6592420, 6684340, 7332940, 7581040, 9364568, 10644308, 11303620, 12920684, 12988520, 13260220, 13822340, 14867164, 15821648, 17958320, 18111340, 18863420, 19358780, 19414196, 23046308, 25998046, 29470480, 31760504, 34385876, 35095868, 36143852, 38610608, 39032726, 39206384, 39519704, 47911340, 48083248, 49354256, 60643180, 66134224, 66681784, 78964744, 80377180, 83591363, 91194020, 102291440, 104160184, 104382260, 109847764, 113881144, 117072280, 117390320, 118743887, 122131112, 137585840, 137904164, 139237880, 149134960, 159272464, 161914010, 162997124, 179779004, 180323108, 188881910, 190946480, 192073180, 197307760, 198132368, 201061382, 208135096, 215395352, 230197708, 249001660, 284293060, 296683504, 306301354, 328137296, 346165768, 359298580, 359444560, 370211056, 378907844, 381859216, 403157560, 415895660, 426082370, 465405140, 496287920, 517871944, 555088280, 565928740, 567483376, 588084556, 656793416, 670097624, 680982860, 689923664, 693441890, 698007430, 715636334, 735646280, 829900232, 893487568, 894096020, 1045902520, 1320928112, 1335376024, 1353689960, 1375651504, 1452333220, 1452528980, 1509265520, 1560833204, 1566511384, 1612122460, 1652411812, 1716518060, 1866219340, 1875824240, 2033132152, 2227448680, 2524477540, 2656097240, 3150119284, 3269488460, 3395125780, 3456513680, 3503885452, 3941086340, 4380007372, 4702144210, 5534663224, 5864634988, 6343397564, 6493913828, 6556294420, 6939656308, 7068762320, 7384855172, 7797171830, 7817756360, 7846210232, 8785471364, 9350250928, 9721749380 82 | (none under 10^10) 83 | 3873, 7838, 175451, 503479, 4536219, 3337918774, 4342206531 84 | 1345, 20758585, 978681929 85 | 138, 708, 1306, 2076, 4308, 12516, 13902, 54839, 413782, 2771717, 9900502, 20914052, 22714374, 118554438, 141285732, 144943259, 220488594, 227777556, 555710604 86 | 8229, 73543, 593157, 704883, 3584293, 130495759, 859456221, 3859823659, 3980405481 87 | 7834, 22163, 98546251, 927209534, 7565169481 88 | 47393, 2203193 89 | any prime ---+---------------------------------------------------------------------------- 90 | 3944047 91 | 410, 870, 2479, 3690, 6390, 12510, 27954, 29530, 34110, 75162, 444810, 2644854, 3419833, 3634843, 28541330, 30863570, 134389721, 155588338, 670193226 92 | 704877, 2990903, 6212897, 71988061, 545160039, 7328014327 93 | 206, 1280452, 2230463, 15342754, 3590393674, 9138555034 94 | 7141, 15545, 36655, 42647087, 91210007, 3524199455, 8069207365 95 | 182, 4634, 12153, 28106, 364142, 1266746, 2368318, 2574026, 11936762, 179449634, 539901518, 1198298738, 2725774138, 6310424354 96 | 17773, 657119 97 | 186, 318, 326, 436, 474, 496, 1212, 1696, 2528, 2712, 2976, 5996, 25122, 79553, 105636, 109328, 124952, 133984, 137784, 299344, 304224, 385716, 478614, 703344, 1567712, 3248264, 6230256, 7781208, 13414694, 59706732, 95603696, 262688588, 360576066, 406938864, 473306123, 1182559584, 1248905552, 2638559963, 2832924704, 3423485414, 5080590038, 5222116272, 9291297696 98 | 323, 549, 813, 6381, 12699, 29829, 63351, 177939, 219147, 770081, 1454141, 2919437, 3364029, 5742027, 12788063, 44489393, 101841857, 116765907, 1150861401 99 | 965, 7822, 2893295, 6448709, 96647039, 7304189554 100 | 96833, 2017763 ----+---------------------------------------------------------------------------