Question

When the positive integers a, b and c are divided by 13, the respective remainders are 9, 7 and 10. Show that a + b + c is divisible by 13

Answer 1

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

a = 13q + 9

b = 13q + 7

c = 13q + 10

a + b + c = 13q + 9 + 13q + 7 + 13q + 10

= 39q + 26

= 13(3q + 2)

which is divisible by 13.