5^n=c mod n (2 <= n <= 10^10, 1 <= c <= 100) c | n ---+---------------------------------------------------------------------------- 1 | many 2 | 3, 123, 202884639, 242405133 3 | 22, 77, 242, 371, 16102, 45727, 73447, 81286, 112277, 368237, 10191797, 13563742, 30958697, 389974222, 6171655457 4 | 4769, 8563651 5 | any prime 6 | 15853, 5520343, 111966563, 2232207889, 5551501871 7 | 114, 822, 4814, 105439, 2511426, 2999454, 2221484158, 2956542126, 6951803986 8 | 9, 39, 369, 603, 711, 48243, 808119, 2991547, 11400519, 16933947, 24096267, 27036711, 43861827, 45975169, 89959311, 99088641, 140584827, 145725849, 185666871, 347834799, 435441591, 608653917, 721842039, 727215399, 918810369, 1155282173, 1958179431, 5289713507, 5341909599 9 | 28, 44, 154, 484, 742, 1256, 2488, 3598, 3674, 23048, 28924, 32204, 33628, 57484, 91454, 146894, 162572, 201014, 224554, 267398, 376808, 680504, 736474, 882968, 2208308, 2804486, 2928299, 5082028, 6004504, 7969448, 20383594, 27127484, 42082984, 61917394, 119902906, 134277319, 181473674, 189076744, 215968984, 246975646, 280189922, 285125324, 311736808, 328762004, 344631368, 416537882, 779948444, 880178024, 957365794, 1170483464, 1876203374, 2638208324, 2662198924, 3239449994, 5882538959, 6451698232, 6978374482, 8805114824 ---+---------------------------------------------------------------------------- 10 | 35, 119, 445, 3395, 6755, 18443263, 272173927 11 | 14, 57, 43707, 3767871, 7564054, 129790527 12 | 1328467 13 | 68, 3604, 7806, 47897, 769116, 3068341, 5463732, 107214769, 244140612, 262043681, 1039324177 14 | 111, 3797643, 109836287, 2955831987 15 | 1555, 117277, 1033810, 9765610, 11964430, 38882395, 109999678 16 | 9569200211 17 | 76, 161, 752, 2043, 2151, 6928, 117724, 195304, 371884, 534317, 7497808, 46338681, 169096089, 287415279, 580530658, 873244048, 1543883258, 5681513819, 9126811048 18 | 2030227, 825910387, 2077330853 19 | 49, 102, 343, 16219, 18054, 18079, 7120998, 9642546, 10763394 ---+---------------------------------------------------------------------------- 20 | 21, 105, 115, 649, 3171, 6693, 12549, 17259, 47289, 74995, 85567, 125265, 159915, 167415, 194019, 390615, 663987, 1047849, 1816105, 2208927, 5178549, 6801085, 13697535, 16779085, 21644799, 45931267, 46701285, 52849785, 68359389, 131701395, 137509095, 180034197, 271794095, 452557585, 544011735, 878410895, 895727973, 1044950865, 1147469485, 1380227529, 1417207533, 3209305539, 6605189535 21 | 299, 604, 47846, 4629469123 22 | 1097122717 23 | 51, 323, 68446, 8738926 24 | 546707, 92316157, 6492324847, 6684849481 25 | many 26 | 27, 33, 1593, 6183, 38973, 57611, 60277, 140319, 651033, 1590637, 2721543, 52245731, 2243656809, 7567168269 27 | 121, 92686, 2124578, 29989366, 78218167 28 | 529, 731, 9131, 11611, 21299, 30533, 98591, 19077601, 43720349 29 | 596, 505289, 3260461, 3628923, 8953708 ---+---------------------------------------------------------------------------- 30 | 3095, 230155, 229421155 31 | 138, 539, 678, 2303, 3349, 8789, 46033, 71222, 273329, 27847342, 361744037, 553789702, 2530080894, 4177817754, 6758041829 32 | 93 33 | 136, 148, 2872, 20561, 90979, 155757083, 302839748, 351617512, 935983228, 5090881957 34 | 34723, 411307, 89268727, 113289059 35 | 45, 515, 3405, 3495, 4066, 31323, 32055, 195309, 365570, 464231, 1521389, 9765590, 19974957, 33215271, 555877695, 2170702519 36 | 589, 12679, 39649, 775651, 7899079, 49818479, 109518691 37 | 198, 1476, 2598, 8668, 20106, 82692, 137148, 169268, 386092, 1052238, 3583678, 8929723, 14947014, 27126732, 49224943, 79240492, 155233062, 321641556, 364751028, 494650076, 2365253756 38 | 87, 106737, 2101137, 7767231, 13182207, 20537637, 1039802561 39 | 18142961, 926081573 ---+---------------------------------------------------------------------------- 40 | 595, 679, 3085, 24205, 131047, 278035, 1547809, 4060711, 12853543, 31937281, 46572965, 76956565, 96234631, 2815277395, 3465186151, 7132125805 41 | 292, 3297, 390584, 489416, 14509887, 111263817, 4521735886, 4532710407 42 | 319, 869, 1691, 13439, 1254915479, 6418953421 43 | 318, 714, 79297, 7839067, 13071743, 36003702, 65339466, 483379954, 1900056058 44 | 117, 150237, 235107, 17691349, 33602153, 67039733, 776172657, 3090796917, 8561879097 45 | 55, 110, 116, 220, 1265, 2765, 6215, 7205, 8855, 22715, 45899, 60817, 64379, 82445, 231935, 336820, 364595, 443890, 758135, 3128345, 3590195, 3923795, 17344415, 17689207, 20793685, 61146305, 199055945, 232987135, 266095358, 502368515, 519402895, 525216587, 868017590, 1141957355, 2298147005, 5759471795, 6589246895, 7260274511, 8164285067, 9274928135 46 | 20485243, 147992953 47 | 91, 1079, 232483, 2295337, 26754133, 50614898, 75854829, 89545703, 3451546527, 4863216583 48 | 1133, 14219, 16153909 49 | 66, 176, 228, 354, 368, 632, 696, 824, 912, 1644, 3088, 3404, 5016, 6556, 9628, 10488, 10846, 11724, 62252, 111991, 115896, 136356, 154348, 210878, 251312, 294006, 347216, 352388, 405668, 616496, 756426, 1080606, 1161192, 1735948, 1832568, 2495566, 4419858, 4855944, 5022852, 5998908, 6052944, 6383256, 6390642, 8875856, 10276072, 14313008, 22950192, 23165552, 25122288, 29939398, 41675784, 43579112, 44452362, 49074834, 57843312, 58713168, 60446669, 62768392, 107951096, 124109486, 140940572, 147744336, 168529966, 168870966, 181522121, 209664354, 225280616, 238246256, 317673299, 382941732, 732421896, 821398988, 823886772, 969673386, 985790154, 1242723086, 1464520046, 1495481776, 1673423372, 1976916738, 2249571336, 2254380656, 2506645816, 2670730896, 2831700036, 3331614256, 3696050116, 3924158456, 4442968316, 5913084252, 6360351332, 6897904008, 7491220176, 8303374596, 9044017608 ---+---------------------------------------------------------------------------- 50 | 75, 205, 1025, 60675, 122025, 143805, 548785, 636645, 2987135, 6936585, 52768025, 58484245, 469682025, 864812615, 8148587025 51 | 2158, 5954, 43498, 15943018, 21304183, 43203238, 47180614, 140646142, 1574870558, 3286508386, 3579889222, 7982457286, 8982472493 52 | 707, 5411, 26167, 35533319, 404268661, 1793314187, 5234978513 53 | 99, 374, 1233, 1462, 3068, 4004, 4292, 7532, 7634, 50517, 67844, 165956, 181012, 302013, 19268469, 25776674, 52160732, 73671884, 150716804, 498276844, 629417643, 1090788646 54 | 133, 2527, 2385103, 77404937, 543822583, 4701324853 55 | 90, 230, 270, 1038, 1242, 1535, 2538, 17130, 38551, 53190, 122526, 141530, 689035, 3051410, 5442202, 7828410, 33607170, 44297010, 47786870, 415368139, 1981577310, 3381328674, 3797445846, 3829909165, 6167769935, 8231007570 56 | 69, 3589, 22839, 11998353, 297036489, 1788396481 57 | 284, 64787, 64894, 390568, 951094, 1418828, 2748596, 5664664, 23715704, 63198449, 81030157, 447624046 58 | (none under 10^10) 59 | 30359, 941698, 1321682, 12788303, 44933618, 1265063482 ---+---------------------------------------------------------------------------- 60 | 1495, 3065, 11635, 49717, 3144767, 4085591, 14679535, 42601141, 159782051 61 | 188, 391, 2748, 7782, 33281, 73267, 1066116, 1198007, 1488991, 6380534548 62 | 63, 261, 361, 987, 1387, 5617, 5901, 9621, 9717, 28203, 205697, 208539, 2718513, 29062467, 41459859, 56358587, 115378137, 1112226381, 1523795217, 2114950707, 2875508433, 4017633417, 4267479379, 4721038389 63 | 841, 21913, 183481, 5224222, 1632070903, 2097393943, 6960754903 64 | 14509, 407209, 12087889, 51009811 65 | 70, 80, 85, 112, 160, 280, 320, 345, 448, 901, 1120, 1160, 1328, 1445, 9280, 10024, 13040, 15610, 19528, 137792, 185584, 186405, 207133, 348770, 2123861, 2125520, 3473680, 6565744, 18746560, 27998656, 41577760, 45786592, 57735958, 120161991, 149313728, 149669720, 183597955, 195142960, 305865320, 331712805, 333469508, 723176420, 813887878, 1454754376, 2067709880, 6451218890, 6844324768, 7019322832 66 | 276391, 546413, 73760327, 163443367, 6250106623 67 | 98, 15558, 90946, 173726, 311489, 4553906, 25708134, 46996914, 53429554, 2068949167 68 | 1083, 129333, 1005789, 1075647, 2402247, 4241293, 5226487, 403885981 69 | 556, 267212, 575846, 2285083, 8336812, 254264252, 490867652 ---+---------------------------------------------------------------------------- 70 | 169, 235, 845, 1648933, 1704365, 2281969, 8177065, 6183236135, 8652352463 71 | 34161, 72831, 321871, 356631, 976527, 4577087, 6607161, 16805717, 18710829, 143202933, 6810092638 72 | 251569, 13903157 73 | 92, 666, 3382, 3634, 5748, 9054, 42541, 44028, 55523, 84948, 130184, 391896, 2710836, 3339011, 5515727, 23284026, 25621254, 49805208, 64936584, 103169717, 1454901386, 4051927158, 4864917546 74 | 18003, 10507197 75 | 175, 305, 1034, 1561, 7075, 10534, 50575, 64225, 98707, 141025, 145325, 872015, 1428766, 1736975, 1953110, 2293925, 12369275, 22381675, 28896050, 40485487, 40591535, 48811774, 69732985, 224870575, 1195146943, 2515040705, 3894717935 76 | 23501, 64343, 6242311, 33922451, 4401613121 77 | 442, 548, 1258, 15982, 48922, 111964, 1366844, 21735374, 28135762, 39107242, 79437131, 174852938, 673799943, 6516908294 78 | 437504363 79 | 5782, 15546, 21311, 50851, 589566, 1512322, 24223422, 121561338, 3247693246, 4210657566, 7203594102 ---+---------------------------------------------------------------------------- 80 | 81, 135, 145, 153, 207, 245, 297, 333, 405, 665, 957, 1269, 1513, 1665, 2997, 5453, 9315, 12665, 13653, 14499, 14895, 14985, 17649, 22589, 22977, 25193, 29049, 29997, 36279, 52515, 56735, 59445, 62613, 112785, 125415, 130215, 164169, 168633, 169047, 198855, 205671, 234765, 254745, 285777, 301257, 302697, 364905, 367893, 392465, 434565, 583865, 615417, 764645, 828927, 874935, 1171815, 1221705, 1507943, 1622745, 1653345, 1975689, 2114235, 2518985, 2528645, 2809665, 2890053, 3182565, 3219777, 3400145, 3564765, 3827169, 5220315, 6022545, 6638265, 6768969, 8205343, 8657469, 10870785, 15283449, 15365645, 15795981, 16651217, 17996985, 18736065, 20735595, 22897657, 23414345, 27946089, 28926045, 29434617, 31530105, 32340465, 34711161, 41888273, 46052645, 48011045, 50389533, 52343289, 53645249, 54807881, 55163785, 56269791, 56301309, 57045897, 57064365, 58819277, 61397745, 64694313, 68730241, 74499465, 78002973, 87928505, 103738185, 108508505, 115595289, 128961909, 135224049, 136625481, 136952937, 140647545, 146561445, 158285745, 165745089, 171443385, 171857295, 172734947, 190712097, 200156105, 228427113, 233910009, 258351845, 259631109, 304619777, 320765577, 374168409, 378821817, 471249945, 482277155, 491367735, 494157797, 522163185, 575092195, 586258497, 598400305, 613278785, 630304065, 672463295, 719503497, 728652865, 729229185, 732380553, 822413097, 880939545, 901255145, 922653257, 959852353, 983982385, 985891905, 1025421777, 1032608169, 1097431137, 1182956865, 1345966445, 1434454941, 1467519305, 1481604047, 1482266601, 1595617785, 1601233497, 1631259405, 1652463953, 1700964697, 1784526693, 1809508985, 1832371713, 2023258553, 2070176805, 2184068745, 2239409667, 2681464185, 2696581769, 2789366585, 2996271297, 3488470539, 3517611755, 3543181817, 3546415305, 3617010693, 3639726809, 3687130449, 4027281369, 4189161645, 4240956257, 4339712835, 4363001361, 4703253065, 6577156665, 7124595705, 7464472689, 7883820749 81 | 88, 308, 968, 1484, 2512, 2536, 2768, 4634, 4976, 6364, 7196, 7348, 8228, 18064, 42824, 46096, 57848, 64408, 67256, 75988, 78134, 114968, 130094, 138488, 182908, 293788, 325144, 355166, 402028, 449108, 534796, 753616, 816068, 943652, 1361008, 1472948, 1534148, 1765936, 1894618, 3295024, 3426404, 4355524, 4416616, 5608972, 5856598, 10164056, 12009008, 15552484, 15938896, 20404984, 37673678, 40767188, 47034056, 48307834, 54254968, 73606256, 84165968, 90932908, 104007344, 105398426, 108337924, 123834788, 146170178, 176941688, 203631868, 214330084, 239805812, 268554638, 271664924, 298801364, 315880888, 316808008, 362947348, 378153488, 431937968, 493951292, 539646778, 560379844, 570250648, 593850236, 623473616, 638188972, 657524008, 689262736, 731872274, 833075764, 833705264, 971396668, 1015983848, 1330996552, 1544689876, 1559896888, 1599705292, 1644113414, 1760356048, 1914731588, 1990407818, 2309438348, 2340966928, 2585859824, 3045547868, 3752406748, 5240789048, 5276416648, 5324397848, 5688099244, 6478899988, 6586505288, 6946486484, 7403956318, 7769815642 82 | 8371, 78043, 990562069 83 | 273, 483, 2494, 23101, 37669, 2848209, 162596711, 363573118, 476857618 84 | 1536803, 503368603 85 | 95, 210, 222, 420, 690, 1554, 2270, 2390, 2670, 13660, 14154, 32676, 34230, 61410, 105260, 142356, 458430, 474330, 639660, 985910, 1000860, 1259706, 1548718, 1851055, 2843564, 5339166, 12901974, 28605882, 44783340, 77618604, 164365230, 257891910, 308021226, 362964252, 936945492, 1235486562, 1318610244, 2596884947, 3095327130, 3149079990, 4466646348, 5367666599, 9715786638 86 | 87659, 8343129, 9925129, 65183963, 1104227823, 1763237723, 8169752697 87 | 649481, 7806878, 23507813, 165971303, 1261676938 88 | 5767 89 | 268, 17884, 47679, 73233, 160011, 390536, 488259, 916264, 29152293, 1603885831, 2778966776, 7021404868 ---+---------------------------------------------------------------------------- 90 | 3035, 18409, 1562767, 10203365 91 | 5178, 36149, 464689, 258795674, 1734469866 92 | 4089, 356497, 2202639, 4509471, 30931807, 94875087 93 | 506, 6061, 66946, 69076, 819028, 917218, 1144066, 2623346, 13591666, 70632994, 105575809, 188532476, 193686694, 257011708, 1037187076 94 | 2972023, 3680579, 257401907, 262815173, 2865833483 95 | 505, 1905, 6946, 59570, 2647946, 9765530, 18625666, 120147945, 172175847, 174623498, 2773369605, 3858004430, 4809712729, 7327667063 96 | 1099, 10673, 1296841, 3445081, 7440203, 10964317, 6280745131, 7097365031 97 | 264, 904, 1068, 1896, 3296, 3882, 4848, 17648, 69234, 238937, 263496, 533644, 583374, 685788, 903193, 1168586, 2135264, 2782614, 3346464, 4922124, 9595952, 23056496, 38206624, 44818548, 92461664, 95030688, 234150456, 400740359, 780921816, 1210719784, 2506683576, 6604218104, 8212928078 98 | 1147, 1953027, 4834959, 6695991, 1478248237 99 | 1963, 44714, 204326, 220571, 28746791, 49973807, 52546819, 264434021, 335529841 100 | 275, 725, 1045, 2755, 35641, 14699411, 24359995, 98859695, 104662525, 126853045, 133479725, 174978275, 410095895, 2009706655, 2304645695 ----+---------------------------------------------------------------------------