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When does this sequence has integer values?

Source: Iranian National Olympiad (3rd Round) 2003

January 24, 2009
inductionnumber theory proposednumber theory

Problem Statement

Let a_1\equal{}a_2\equal{}1 and a_{n\plus{}2}\equal{}\frac{n(n\plus{}1)a_{n\plus{}1}\plus{}n^2a_n\plus{}5}{n\plus{}2}\minus{}2for each n∈N n\in\mathbb N. Find all n n such that an∈N a_n\in\mathbb N.
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