Question

Prove for all integers a and b, if a mod 8 = 5 and b mod 8 = 3 then ab mod 8 = 7.

Answer 1

Since $a \mod 8 = 5$ and $b \mod 8 = 3,$ it follows that $ab \mod 8 = 3 \cdot 5\mod 8 =15\mod 8 =7.$