Track / Stage 6 / 1 of 400 #1001 of 1964

Positive integers $p$, $a$ and $b$ satisfy the equation $p^2 + a^2 = b^2$. Prove that if $p$ is a prime greater than 3, then $a$ is a multiple of 12 and $2(p + a + 1)$ is a perfect square.

This one wants a proof. Work it on paper, then check yourself against the publisher's own solution, linked below. Be honest about it: the record is only any use to you if it is.

I solved it I didn't Skip

Next problem →

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; question papers published free at bmos.ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.