OIM 1992 Problem 4

Let $\{a_{n}\}_{n \geq 0}$ and $\{b_{n}\}_{n \geq 0}$ be two sequences of integer numbers such that:

i. $a_{0}=0$ , $b_{0}=8$ .

ii. For every $n \geq 0$ , $a_{n+2}=2a_{n+1}-a_{n}+2$ , $b_{n+2}=2b_{n+1}-b_{n}$ .

iii. $a_{n}^{2}+b_{n}^{2}$ is a perfect square for every $n \geq 0$ .

Find at least two values of the pair $(a_{1992}, b_{1992})$ .