Let $a$, $b$, and $c$ be integers satisfying $a^2 + b^2 = c^2$. Prove: $abc$ must be even. I'm pretty sure that this can be proved by reductio ad absurdum, and have a proof for that. However, I'm not sure how to prove...--prophetes.ai

Let $a$, $b$, and $c$ be integers satisfying $a^2 + b^2 = c^2$. Prove: $abc$ must be even. I'm pretty sure that this can be proved by reductio ad absurdum, and have a proof for that. However, I'm not sure how to prove this using any other method of proof. It's my first time taking a course in logic and I'm not sure where to go with this.

Hint: Think about even and odd numbers. Can all 3 variables be odd?