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Part of 1995 Czech and Slovak Match

Problems(1)

Czech-Slovak 1995!

Source:

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\geq 1

. Do there exist

p,q,r

so that a_pa_q \equal{}a_r?

algebra proposedalgebra