IMO Shortlist 2009 problem N4


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2. travnja 2012.
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Find all positive integers n such that there exists a sequence of positive integers a_1, a_2, ..., a_n satisfying
a_{k+1}=\frac{a_k^2+1}{a_{k-1}+1}-1 for every k with 2 \leqslant k \leqslant n-1.

Proposed by North Korea
Izvor: Međunarodna matematička olimpijada, shortlist 2009