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CN-SMO 2013 Problem 3

    A sequence {an}\{a_n\} , a1=1,a2=2,an+1=an2+(−1)nan−1a_1=1,a_2=2,a_{n+1}=\dfrac{a_n^2+(-1)^n}{a_{n-1}} . Show that am2+am+12∈{an},∀m∈Na_m^2+a_{m+1}^2\in\{a_n\},\forall m\in\Bbb N

    Dataset text AI-MO AoPS. Quoted with source.

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