53^n=c mod n (2 <= n <= 10^10, 1 <= c <= 100) c | n ---+---------------------------------------------------------------------------- 1 | many 2 | 3, 15, 17, 35, 95, 1191, 44897, 83507, 810683, 1928633, 36324555, 1330982555, 4652832715 3 | 5, 46, 122, 205, 2958622, 37400618, 86855005, 400733113 4 | 7, 7056781, 2272168549, 2806576727 5 | 44, 1402, 1556, 1844, 18609, 56859, 95799, 137324, 278198, 282579, 3384202, 4045799, 4527849, 10134983, 11712543, 15472916, 19085961, 26537482, 30466964, 44212202 6 | 47 7 | 23, 934, 1975, 2294, 16075, 21275, 48794, 62198, 123194, 253362, 524886, 1525103, 12862555, 36051335, 47586674, 321975806, 730475215, 8719183038 8 | 9, 21, 45, 51, 63, 105, 285, 417, 565, 3573, 6867, 16485, 17751, 21105, 35679, 41031, 65331, 134691, 250521, 325191, 411205, 1326843, 1353237, 1878891, 2432049, 2580165, 2839431, 2973411, 4042773, 5601561, 5651247, 5785899, 12163179, 42830739, 48957765, 63994179, 108973665, 234081099, 244870227, 307422045, 331255071, 372876651, 674424051, 837191571, 884717043, 1293444285, 1616431959, 2240326977, 3992947665, 6604891061, 8004089619, 8041347867, 9109966383, 9499139523, 9622486251 9 | 10, 11, 14, 56, 76, 92, 119, 121, 148, 244, 410, 664, 1358, 1610, 2812, 4630, 4796, 5951, 6776, 9023, 11224, 11656, 14276, 15466, 18202, 19462, 22030, 24376, 24458, 74632, 80764, 142006, 162542, 173476, 224590, 230728, 244156, 304510, 324566, 380264, 415352, 426376, 548932, 1399330, 1638014, 1747052, 1810886, 2254424, 2798306, 3014101, 3585170, 4072376, 4544744, 5917244, 7595032, 7830830, 9886684, 9940028, 10337368, 15427016, 20188696, 21001816, 33346504, 39913528, 40381628, 52043512, 56949746, 60797176, 69398296, 74801236, 79393666, 91965394, 93813923, 173205410, 173710010, 187084876, 214542196, 300370136, 404515370, 448142323, 522744370, 676075996, 767496970, 781445110, 782928436, 801466226, 881396390, 899526590, 1013636792, 1021213096, 1306834070, 1938544996, 2098454926, 2475203210, 2956508408, 3009898084, 4706289676, 5050601636, 5492863864 ---+---------------------------------------------------------------------------- 10 | 43, 249043 11 | 129, 1731, 2798, 3829, 27219, 32746, 2050119106, 3670559809 12 | 41, 55, 295, 292895, 9393047, 80925407 13 | 102, 466, 618, 2263, 3569, 9844, 168085, 276998, 1359286, 1457004, 2630156, 2823907, 6329058, 12202874, 81038868, 563210022, 572962487, 940026198, 9555145134 14 | 33, 39, 143, 949, 1041, 1417, 3341, 5093, 38623, 84279, 445029, 583271, 2894411, 73880873, 508538081, 1313177723, 3439432763, 5222790023, 8587768839 15 | 19, 22, 254, 1135957, 3176987, 17430389, 29874253, 44105791, 4188329387 16 | 37, 319, 2519 17 | 115, 344, 698, 2008, 2481, 2648, 3664, 21232, 44589, 57087, 59152, 986308, 1105616, 2525335, 2535622, 8713784, 15411184, 305314952, 437931664, 4882365188 18 | 25, 49, 343, 1225, 13573, 24325, 127645, 336385, 931525, 34327825, 124157425, 503777449, 876282925, 2451364405, 6377271565 19 | 30, 62, 90, 1510, 2466, 21702, 128286, 337842, 408522, 1439530, 5971230, 6315679, 15469290, 30086594, 200557314, 893960890, 1387863870, 2238954010, 2243887090, 3413042671, 6088855818, 7246712938 ---+---------------------------------------------------------------------------- 20 | 87, 177, 5359, 28900201 21 | 34, 82, 97274, 322060, 1578092, 18930826, 365924140, 1990021420, 4070164222, 5437339979 22 | 31, 419737, 110237581, 2090977355, 3617753159 23 | 165, 398, 1169, 1253, 1345, 2807, 3365, 3405, 32505, 74427, 167145, 2331094, 7850387, 8380705, 23097494, 74602934, 110405309, 246154913, 462717785, 5246525633 24 | 29, 5332387, 65538173 25 | 28, 58, 88, 268, 322, 492, 1284, 2804, 3048, 3112, 3688, 4543, 6456, 14852, 21288, 24828, 35688, 37218, 37598, 44488, 56136, 62616, 108866, 113718, 121748, 138504, 191598, 242696, 274648, 359368, 446646, 535694, 556396, 565158, 2105656, 2462236, 5101448, 5215692, 5235576, 5649028, 6768404, 7020068, 8091598, 9055698, 10104564, 10520648, 12500572, 19883542, 20269966, 23425086, 25220154, 30945832, 32137788, 38171922, 47233042, 48128474, 49957854, 53074964, 60933928, 68703754, 85909064, 88424404, 96199514, 121690408, 183149868, 212895096, 232951598, 340242312, 365554252, 400043416, 661646904, 692788836, 698433884, 753496012, 765570732, 864598652, 1101141118, 1398193972, 2331608902, 3550600492, 4496328552, 5471239708, 5928835592, 6527162488, 7232190936, 9076635402 26 | 27, 111, 297, 447, 1359, 14943, 254497, 10929621, 18887607, 67517859, 101134627, 132743901, 5528756601 27 | 214, 1586, 70174, 112606, 115817, 581614, 1307695, 3281023, 18768794, 39461609, 389513426, 604329814, 1064935106, 1730676506, 3703800035, 4927010374, 6650134966 28 | 365, 5728705, 14628637, 192595727 29 | 278, 861, 1329, 2247, 3149446, 7890452, 13055781, 73641723, 177069117, 199839633, 581414902, 948003577 ---+---------------------------------------------------------------------------- 30 | 203, 1421, 45563, 154889, 310793, 5231513, 9038981, 18909653, 26891837, 128880437, 531071141 31 | 66, 926, 42074, 383462, 12060961, 37653614, 47854423, 142405558, 183176538 32 | 75, 133, 175, 475, 3535, 4555, 5955, 6775, 12315, 29769, 322615, 417535, 4053415, 10086715, 10966795, 16310113, 181622775, 279414475, 4074968695, 4892802271, 6254786271, 6654912775, 6842447395 33 | 68, 185, 694, 1184, 2516, 2965, 4765, 27158, 67616, 116036, 1918265, 2295476, 2408984, 25844792, 58859048, 249158188, 813732448, 2920752116, 6642694988 34 | 2461, 12581, 1756189 35 | 38, 146, 531, 5571, 24807, 223299, 356914, 8541146, 21175839, 4862831343 36 | 3223, 52519, 14318953 37 | 77, 132, 155, 564, 596, 5884, 17549, 26092, 221124, 830772, 891989, 2311742, 2820092, 5305746, 13080515, 13422756, 15366804, 22745492, 60415372, 63040644, 67690172, 82811855, 205331502, 834298524, 3694060182, 7891274806 38 | 148839, 310965, 506239, 2084683, 75314459, 167871779, 173280899, 1210782813 39 | 70, 554, 3470, 36589, 43286, 18505930, 38906330, 139686130, 207070718, 252023074 ---+---------------------------------------------------------------------------- 40 | 762677, 3036527, 290257907 41 | 237, 346, 471, 920, 2872, 31089, 137512, 301989, 472084, 789044, 976964, 1160392, 2017864, 3601996, 27321292, 4760871033 42 | 13651, 253217, 3262055, 11602481, 24972503 43 | 527, 922, 53045, 940002, 102270462, 127908002, 3166337298, 3690260238 44 | 69, 2157, 151839, 292823, 412391, 15508703, 127381521, 531137621, 8658871531 45 | 116, 1004, 1084, 1382, 31378, 65621, 166762, 401636, 5055356, 211618684, 605315404 46 | 8465130079 47 | 123, 418, 555, 2762, 12133, 19958, 21293, 26529, 103598, 888998, 4274174, 331581566, 387234262, 1159480635, 1518554242 48 | 1067, 418195445, 1131854545 49 | 50, 114, 150, 264, 290, 456, 493, 552, 592, 696, 830, 1112, 1868, 1914, 2712, 2850, 3576, 3918, 3950, 4350, 4588, 5430, 7064, 7636, 8322, 8936, 16530, 17232, 23024, 26004, 31236, 32150, 33590, 42550, 42864, 43548, 49213, 59664, 75688, 75696, 78648, 89034, 89322, 97588, 124396, 135888, 139548, 140676, 184152, 192932, 202044, 208050, 211048, 246388, 295944, 312994, 320550, 357450, 403644, 447450, 470042, 494196, 506724, 624450, 627154, 775024, 817550, 921488, 1049772, 1136784, 1283974, 2326264, 2460244, 2464304, 2516550, 2940234, 3050206, 3097950, 3451472, 4309950, 4502202, 5026036, 5054970, 5849890, 6015504, 6823344, 7871888, 13492610, 15854550, 17140796, 18768396, 22074510, 25725110, 25751652, 29219088, 29324770, 30658350, 33163170, 36069148, 39507290, 39838837, 47735130, 65482314, 69293884, 72102670, 77911984, 82795578, 95173348, 111356682, 114427470, 119683014, 145625156, 148006770, 244519102, 250488944, 298679988, 309615664, 309788502, 345842404, 431111050, 437702988, 442286952, 515506904, 517971768, 576159364, 602143930, 607307586, 612030392, 619814824, 623373479, 643951612, 664208430, 773268612, 906642264, 1025437650, 1104471728, 1131817776, 1135893264, 1194532944, 1262319556, 1347151110, 1460950430, 1606906992, 1779401508, 2253992016, 2416297592, 2672075892, 2741061450, 2839423408, 2977171448, 3340403958, 3430034736, 3794961210, 3920533364, 4099100568, 4580711124, 4989918013, 5166548263, 5291204208, 5890186984, 9528831474 ---+---------------------------------------------------------------------------- 50 | 57, 147, 399, 1119, 2793, 6909, 185577, 4309599, 838299021, 938108031, 1667792469, 4090397587 51 | 161, 329, 394, 96698, 1916449, 129179162, 1703178806 52 | 335, 115235, 14946695, 31208615, 97837835, 167582903 53 | any prime 54 | (none under 10^10) 55 | 306, 15894, 22734, 23874, 76794, 92786, 192414, 267678, 352494, 432486, 982482, 2690262, 5859859, 8907462, 11936754, 17799786, 22227274, 346543674, 348893618, 2276856954, 3479840778, 6301571018 56 | 339, 1317, 5037, 70503, 209397, 11159557, 17239461, 371238187 57 | 86, 236, 292, 775, 916, 3415, 15655, 108475, 129215, 136589, 219515, 1690175, 2418775, 4721455, 94641475, 123020281, 236397899, 396203375, 3501473555, 3891667448 58 | 473, 917, 959, 36287, 522065, 912677, 59742205, 304041437, 344417623, 513482927, 3274130581 59 | 187, 230, 2167, 4377, 49407, 51559, 349082, 762857, 2456770, 5354822, 6540230, 6817087, 7328471, 8751651, 8981438, 17107526, 26987917, 27120651, 345936333, 354679347, 480922163 ---+---------------------------------------------------------------------------- 60 | 209, 553, 4859, 10727, 264233, 266959, 23681119, 27810727, 874691839 61 | 458, 4978, 9564, 10020, 101180, 291306, 526028, 1236588, 2426118, 2612674, 2689964, 2706260, 3877894, 6183418, 7198291, 9684998, 25831012, 234604542, 733944268, 771885798, 816861307, 6986376517 62 | 747, 4035, 9921, 87921, 123015, 138843, 263799, 8111115, 232330795, 279333567, 295124919, 1198080495, 1626715071, 7190421795 63 | 2645, 2746, 528893, 869326, 2620333, 3416923, 9091205, 24237754, 6878897065 64 | (none under 10^10) 65 | 224, 668, 11812, 14272, 15604, 23084, 33248, 37203, 159496, 535862, 716433, 815759, 2831181, 13381696, 23889257, 88734758, 96341273, 111529336, 292174391, 300227984, 321192632, 454314656, 493720277, 981176168, 1075789119, 2521714029, 7984838456 66 | 221, 299, 23069, 2097043, 1167125063, 1988540069 67 | 914, 931, 1038, 1866, 2695, 5635, 29149, 39655, 73735, 108955, 309913, 370195, 411954, 1383979, 5644849, 17437483, 31646062, 103856755, 182844235, 240924037 68 | 125, 445, 21545, 29125, 39125, 148809, 152025, 207905, 313725, 1240325, 2994045, 5132625, 11874405, 12163625, 46914005, 51460725, 807955131 69 | 274, 3058, 8110, 5041964, 7890412, 8414162, 41912804, 95830459, 605378623, 1185684538 ---+---------------------------------------------------------------------------- 70 | 13073, 280993, 8260909, 38556727, 86159011, 177553121 71 | 74, 99, 3543, 3717, 4431, 29993, 33039, 117081, 133749, 284949, 448677, 745353, 3985401, 4112187, 22514847, 33394011, 132658449, 519247647, 585916502, 1833532923 72 | 2135, 2155, 6767, 8227, 19523, 7116355, 30485615, 589672139, 2852880455 73 | 138, 762, 1656, 3084, 47448, 158082, 438356, 1116792, 2467096, 5245852, 12127186, 40411044, 46298632, 108832536, 304646814, 412390632, 694869332, 962110692, 1416263707, 1602713734, 3632502392, 9888397307 74 | 579, 771, 1099, 1897, 139983, 149327, 294577, 400141, 32967013, 61605859, 698269029 75 | 2734, 955897 76 | 151766543, 474361361, 2744691269 77 | 93, 255, 1366, 3788, 5559, 8332, 12223, 131415, 1887855, 4687022, 24120127, 68939243, 933793563 78 | 4883, 125785, 129305, 2227279 79 | 98, 130, 182, 282, 390, 602, 1274, 1542, 4214, 5646, 7826, 8034, 10661, 14651, 33202, 54782, 54929, 115446, 131537, 193781, 243438, 334126, 451430, 625730, 1217190, 1502291, 2377193, 4609662, 5617430, 6616883, 31308599, 50085438, 94647371, 117691301, 190837271, 379383703, 941529953, 980472143, 1048427471, 1421399630, 3527173182, 3961602470, 4681403970, 7371512330, 7583073134, 8799066510 ---+---------------------------------------------------------------------------- 80 | 81, 501, 4873, 27813, 28647, 34173, 28058067 81 | 112, 152, 184, 238, 242, 280, 296, 488, 580, 820, 847, 1328, 1462, 1520, 1708, 2204, 2278, 2344, 2714, 2716, 2960, 3220, 5380, 5624, 5636, 5740, 6680, 7502, 7880, 9260, 9592, 11902, 13552, 16402, 18046, 21544, 22448, 23312, 24940, 25940, 28552, 30932, 33428, 36404, 38924, 44060, 48752, 48916, 56240, 69040, 79120, 81697, 112312, 129040, 149264, 161528, 168760, 173456, 208222, 215017, 234422, 274436, 284012, 291640, 325084, 346952, 449180, 461456, 488312, 556780, 589040, 609020, 649132, 650978, 760528, 768340, 830704, 852082, 852752, 1047248, 1097864, 1118320, 1401380, 1455832, 2585462, 2756080, 2798660, 2940020, 3276028, 3420220, 3494104, 3621772, 4359880, 4379452, 4508848, 5357320, 5596612, 6028202, 6034760, 6270032, 7170340, 7922732, 8144752, 9089488, 11823152, 11834488, 12003668, 12192760, 12801020, 13132528, 15190064, 15361508, 15661660, 16115438, 17510102, 19545160, 19773368, 19880056, 20674736, 23226622, 24112520, 25829108, 26325620, 27000182, 29192380, 30854032, 32099012, 36854420, 40377392, 42003632, 46059320, 46134238, 66693008, 67754408, 79827056, 80763256, 93797072, 104087024, 108533680, 113899492, 121594352, 136717780, 138796592, 140164360, 145256012, 149602472, 158787332, 161755852, 162417808, 178213960, 180941840, 183930788, 187627846, 209886512, 211266728, 221706824, 242341352, 268889102, 294568084, 301092902, 335408752, 346410820, 347420020, 368214160, 374169752, 403715420, 410212627, 428634566, 429084392, 454882088, 470677748, 549253360, 549851239, 562190540, 586997324, 600740272, 615386960, 650274952, 663741488, 679192060, 690068644, 719513212, 779517332, 809030740, 857911060, 896284646, 1045488740, 1169005028, 1176833560, 1236618998, 1288549480, 1352151992, 1402255120, 1456097020, 1456519720, 1534993940, 1562890220, 1565856872, 1602932452, 1708830088, 1762792780, 1799053180, 1802932240, 1906062308, 1939434160, 1950992720, 2027273584, 2042426192, 2383292036, 2515518260, 2613668140, 3057224860, 3250529548, 3377209040, 3464271908, 3525529544, 3645188752, 3665036654, 3866542876, 3877089992, 3898303088, 3917661320, 4067075560, 4155772112, 4169000542, 4196909852, 4689173096, 4913434480, 4950406420, 5163367376, 5913016816, 6019796168, 6264026692, 7439390908, 7863759820, 8372620826, 8604466960, 9412579352 82 | 5675, 1195349, 26107499, 2090977055 83 | 85, 94, 345, 1147, 5389, 17854, 56005, 74397, 233914, 300037, 603787, 44493277, 69931965, 222520605, 789546837, 891184738, 2052430582, 6530141803, 8071367701, 9754302507 84 | (none under 10^10) 85 | 276, 454, 678, 36948, 138428, 226716, 289196, 450618, 657762, 4863948, 12655146, 14010342, 101216892, 202528578, 2257513073, 3339025631, 8381831477, 9002203772 86 | 4521, 148791, 55122377, 65733387, 8893029179 87 | 755, 2722, 19601, 2124570755, 4962559055 88 | 785, 8323, 14413, 31465, 70945, 210217, 2663665, 20345605, 34125763, 43600165, 221055265, 252587845, 1558820411, 5540274985, 6561291499, 6981364285 89 | 110, 170, 279, 524, 536, 1179, 3310, 12399, 30116, 36549, 71433, 76504, 335032, 793210, 6219039, 7653544, 14067656, 22188904, 25593723, 30507914, 51700570, 74938277, 87030514, 105490636, 147584030, 231601947, 814965484, 979483594, 1995977439, 2012058999, 2174334069, 4974825638 ---+---------------------------------------------------------------------------- 90 | 236061719 91 | 198, 253, 302, 30967, 4617238, 135271763, 256087567, 959063454, 1192219542, 7388120346 92 | 195, 273, 327, 2355, 3255, 37661, 42315, 87735, 338055, 673827, 912795, 1297815, 4124215, 16871595, 20260695, 21050187, 31691361, 32084535, 48606915, 52278555, 136902495, 197922963, 4453780695, 5457719589, 7792601817 93 | 194, 266, 4298, 6764, 23639, 81662, 142436, 717308, 1087394, 1131602, 1701799, 6609305, 9457028, 9936445, 12517925, 21848225, 51556862, 59718254, 77981684, 134143925, 474361844, 1255645954, 3282456914, 5225141228 94 | 33031, 2523494927 95 | 118, 411, 543, 2191, 33945562, 80431102, 546546259 96 | (none under 10^10) 97 | 176, 226, 355, 356, 438, 744, 1032, 1056, 1504, 1528, 2424, 4246, 4272, 7388, 20395, 65248, 105816, 155464, 174728, 246576, 264648, 270264, 326112, 350292, 358195, 368629, 525264, 836616, 882982, 1690372, 2158115, 6792346, 6900486, 8336712, 10846176, 10909536, 34033296, 44458464, 98944834, 374135604, 536272224, 698063476, 716278452, 2378041936, 2628186144, 4881967266, 6986107488 98 | 183, 545, 813, 1557, 2985, 8847, 31905, 58665, 84033, 307485, 415629, 454023, 111302365, 304236105 99 | 190, 542, 3610, 5350, 14270, 39558637, 348588061, 4181132650 100 | 8870821, 272079647, 1068752059 ----+---------------------------------------------------------------------------