When the positive integers be a, b and c are divided by 13, the respec

1.	When the positive integers be 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» Let the positive integers be a, b, and c. a = 13 q + 9 b = 13q + 1 c = 13 q + 10 a + b + c = 13q + 9 + 13q + 7 + 13q + 10 = 39q + 26 = 13 (3q + 2) Which is divisible by 13.

When the positive integers be 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»

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

a = 13 q + 9

b = 13q + 1

c = 13 q + 10

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

= 39q + 26

= 13 (3q + 2)

Which is divisible by 13.