IMC 1999 — Keystage 3 (IWYMIC) — individual Question 8

Let $a,b,c$ be positive integers. The sum of $160$ and the square of $a$ is equal to the sum of $5$ and the square of $b$. The sum of $320$ and the square of $a$ is equal to the sum of $5$ and the square of $c$. Find $a$.