Question

both m and n are integers. 5m 3n is divisible by 11.what is the remainder when 9m n is divided by 11?

Answer 1

Hello,

9m+n is divisible by 11 (remainder =0)

Since
$5m+3n=11*k\\ m= \dfrac{11*k-3n}{5}\\ 9m=9*\dfrac{11*k-3n}{5}\\ 9m+n=9*\dfrac{11*k-3n}{5}+ \dfrac{5n}{5} \\ 9m+n= \dfrac{99k-27n+5n}{5}\\ 9m+n=11* \dfrac{9k-2n}{5}$