Question

Cate numere naturale de 4 cifre,impartite la 115,dau restul 100?Determinati suma acestor numere.

Answer 1

Din teorema impartirii cu rest :

x = i * 115 + 100.

Luam la rand fiecare i, de la 8 la 86.

Numerele sunt :

1020, 1135, 1250, 1365, 1480, 1595, 1710, 1825, 1940, 2055, 2170, 2285, 2400, 2515, 2630, 2745, 2860, 2975, 3090, 3205, 3320, 3435, 3550, 3665, 3780, 3895, 4010, 4125, 4240, 4355, 4470, 4585, 4700, 4815, 4930, 5045, 5160, 5275, 5390, 5505, 5620, 5735, 5850, 5965, 6080, 6195, 6310, 6425, 6540, 6655, 6770, 6885, 7000, 7115, 7230, 7345, 7460, 7575, 7690, 7805, 7920, 8035, 8150, 8265, 8380, 8495, 8610, 8725, 8840, 8955, 9070, 9185, 9300, 9415, 9530, 9645, 9760, 9875, 9990

In total 79 de numere.

Suma acestora e 434895.