MathDB
IMO Shortlist 2009 - Problem N4

Source:

July 5, 2010
modular arithmeticnumber theoryIMO ShortlistSequenceDivisibility

Problem Statement

Find all positive integers nn such that there exists a sequence of positive integers a1a_1, a2a_2,…\ldots, ana_n satisfying: ak+1=ak2+1ak−1+1−1a_{k+1}=\frac{a_k^2+1}{a_{k-1}+1}-1 for every kk with 2≤k≤n−12\leq k\leq n-1.
Proposed by North Korea
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