1992 OIM Problems/Problem 4

Problem

Let $(a_n)$ and $(b_n)$ be two sequences of integers that verify the following conditions:

i. $a_0 = 0$ , $b_0 = 8$

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

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

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

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

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