This is a part from a homework. I solved all examples apart from this one. So the task is: We know that $3$ divides $a^2 + b^2$. Prove that $3$ divides $a$ and $3$ divides $b$. I cannot think of anything useful. I know that $a^2 + b^2 = (a + b)^2 - 2ab$, but I don't see how it can help me :(
Best regards, Petar