Divisibility

Determine the smallest integer which divided 11 gives remainder 4 when divided 15 gives remainder 10 and when divided by 19 gives remainder 16.

Correct result:

x =  1555

Solution:

x₁: 4, 15, 26, 37, 48, 59, 70, 81, 92, 103, 114, 125, 136, 147, 158, 169, 180, 191, 202, 213, 224, 235, 246, 257, 268, 279, 290, 301, 312, 323, 334, 345, 356, 367, 378, 389, 400, 411, 422, 433, 444, 455, 466, 477, 488, 499, 510, 521, 532, 543, 554, 565, 576, 587, 598, 609, 620, 631, 642, 653, 664, 675, 686, 697, 708, 719, 730, 741, 752, 763, 774, 785, 796, 807, 818, 829, 840, 851, 862, 873, 884, 895, 906, 917, 928, 939, 950, 961, 972, 983, 994, 1005, 1016, 1027, 1038, 1049, 1060, 1071, 1082, 1093, 1104, 1115, 1126, 1137, 1148, 1159, 1170, 1181, 1192, 1203, 1214, 1225, 1236, 1247, 1258, 1269, 1280, 1291, 1302, 1313, 1324, 1335, 1346, 1357, 1368, 1379, 1390, 1401, 1412, 1423, 1434, 1445, 1456, 1467, 1478, 1489, 1500, 1511, 1522, 1533, 1544, 1555

x₂: 10, 25, 40, 55, 70, 85, 100, 115, 130, 145, 160, 175, 190, 205, 220, 235, 250, 265, 280, 295, 310, 325, 340, 355, 370, 385, 400, 415, 430, 445, 460, 475, 490, 505, 520, 535, 550, 565, 580, 595, 610, 625, 640, 655, 670, 685, 700, 715, 730, 745, 760, 775, 790, 805, 820, 835, 850, 865, 880, 895, 910, 925, 940, 955, 970, 985, 1000, 1015, 1030, 1045, 1060, 1075, 1090, 1105, 1120, 1135, 1150, 1165, 1180, 1195, 1210, 1225, 1240, 1255, 1270, 1285, 1300, 1315, 1330, 1345, 1360, 1375, 1390, 1405, 1420, 1435, 1450, 1465, 1480, 1495, 1510, 1525, 1540, 1555

x₃: 16, 35, 54, 73, 92, 111, 130, 149, 168, 187, 206, 225, 244, 263, 282, 301, 320, 339, 358, 377, 396, 415, 434, 453, 472, 491, 510, 529, 548, 567, 586, 605, 624, 643, 662, 681, 700, 719, 738, 757, 776, 795, 814, 833, 852, 871, 890, 909, 928, 947, 966, 985, 1004, 1023, 1042, 1061, 1080, 1099, 1118, 1137, 1156, 1175, 1194, 1213, 1232, 1251, 1270, 1289, 1308, 1327, 1346, 1365, 1384, 1403, 1422, 1441, 1460, 1479, 1498, 1517, 1536, 1555

$$\begin{gathered} 1555÷11=141+{\displaystyle \frac{4}{11}} \\ 1555÷15=103+{\displaystyle \frac{10}{15}} \\ 1555÷19=81+{\displaystyle \frac{16}{19}} \end{gathered}$$

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