Divisibility

Determine the smallest integer which divided 8 gives remainder 6 when divided 19 gives remainder 9 and when divided by 11 gives remainder 2.

Result

x =  750

Solution:

x =
x1: 6, 14, 22, 30, 38, 46, 54, 62, 70, 78, 86, 94, 102, 110, 118, 126, 134, 142, 150, 158, 166, 174, 182, 190, 198, 206, 214, 222, 230, 238, 246, 254, 262, 270, 278, 286, 294, 302, 310, 318, 326, 334, 342, 350, 358, 366, 374, 382, 390, 398, 406, 414, 422, 430, 438, 446, 454, 462, 470, 478, 486, 494, 502, 510, 518, 526, 534, 542, 550, 558, 566, 574, 582, 590, 598, 606, 614, 622, 630, 638, 646, 654, 662, 670, 678, 686, 694, 702, 710, 718, 726, 734, 742, 750

x2: 9, 28, 47, 66, 85, 104, 123, 142, 161, 180, 199, 218, 237, 256, 275, 294, 313, 332, 351, 370, 389, 408, 427, 446, 465, 484, 503, 522, 541, 560, 579, 598, 617, 636, 655, 674, 693, 712, 731, 750

x3: 2, 13, 24, 35, 46, 57, 68, 79, 90, 101, 112, 123, 134, 145, 156, 167, 178, 189, 200, 211, 222, 233, 244, 255, 266, 277, 288, 299, 310, 321, 332, 343, 354, 365, 376, 387, 398, 409, 420, 431, 442, 453, 464, 475, 486, 497, 508, 519, 530, 541, 552, 563, 574, 585, 596, 607, 618, 629, 640, 651, 662, 673, 684, 695, 706, 717, 728, 739, 750









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