Problem

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Tags: algebra unsolved, algebra



A sequence $\{a_n\}$ , $a_1=1,a_2=2,a_{n+1}=\dfrac{a_n^2+(-1)^n}{a_{n-1}}$. Show that $a_m^2+a_{m+1}^2\in\{a_n\},\forall m\in\Bbb N$