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Czech-Slovak 1995!

Source:

January 17, 2008
algebra proposedalgebra

Problem Statement

Let a_1\equal{}2, a_2\equal{}5 and a_{n\plus{}2}\equal{}(2\minus{}n^2)a_{n\plus{}1}\plus{} (2\plus{}n^2)a_n for n≥1 n\geq 1. Do there exist p,q,r p,q,r so that a_pa_q \equal{}a_r?
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