# Prove that \$ a + 2b equiv 0 \$ (mod 3) if and only if \$ a equiv b \$ (mod 3).

I need to prove it $$a + 2b equiv 0$$ (mod 3) if and only if $$a equiv b$$ (mod 3).
I know you have to show both cases, but my teacher said that we were not supposed to use one to solve the other, so I'm stuck.