Question 45
Let $a_{n}, b_{n}$ be two sequences of integers such that:
(1) $a_{0}=0$, $b_{0}=8$;
(2) $a_{n+2}=2 a_{n+1}-a_{n}+2$, $b_{n+2}=2 b_{n+1}-b_{n}$,
(3) $a_{n}^{2}+b_{n}^{2}$ is a square for $n\gt 0$.
Find at least two possible values for $\left(a_{1992}, b_{1992}\right)$.
(1) $a_{0}=0$, $b_{0}=8$;
(2) $a_{n+2}=2 a_{n+1}-a_{n}+2$, $b_{n+2}=2 b_{n+1}-b_{n}$,
(3) $a_{n}^{2}+b_{n}^{2}$ is a square for $n\gt 0$.
Find at least two possible values for $\left(a_{1992}, b_{1992}\right)$.