IMO 1986 LL ROM64

Let (an)n\inN be the sequence of integers defined recursively by

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IMO 1986 LL ROM64

Origin: ROM

Problem

Let (an)n\inN be the sequence of integers defined recursively by a1 = a2 = 1, an+2 = 7an+1 −an −2 for n \geq1. Prove that an is a perfect square for every n.