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IMO Shortlist 2009 - Problem N6

Source:

July 5, 2010
algebrapolynomialSequencenumber theoryDivisibilityIMO Shortlist

Problem Statement

Let kk be a positive integer. Show that if there exists a sequence a0,a1,…a_0,a_1,\ldots of integers satisfying the condition an=an−1+nkn for all n≥1,a_n=\frac{a_{n-1}+n^k}{n}\text{ for all } n\geq 1, then k−2k-2 is divisible by 33.
Proposed by Okan Tekman, Turkey
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