Question

When the positive integers a, b and c are divided by 13 the respective remainders is 9, 7 and 10. Find the remainder when a b + + 2 3c is divided by 13

Answer 1

Let the positive integers be a, b, and c.

a = 13q + 9

b = 13q + 7

c = 13q + 10

a + 2b + 3c = 13 q + 9 + 2(13q + 7) + 3(13q + 10)

= 13q + 9 + 269 + 14 + 39q + 30

= 78q + 53 = (13 × 6)q + 53

The remainder is 53.

But 53 = 13 × 4 + 1

∴ The remainder is 1