jmc

Question

Suppose a and b are positive integers, neither of which is a multiple of 3. Find the least possible remainder when a^2 + b^2 is divided by 3.

Accepted Answer

Note that 1^2 2^2 1 3. The only possible modulo 3 residue for a square that isn't a multiple of 3 is 1. Therefore, a^2 + b^2 1 + 1 2 3.