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Bulgaria 1999 Sequence Problem

Source:

November 14, 2012
modular arithmeticnumber theory unsolvednumber theory

Problem Statement

Let {an}\{a_n\} be a sequence of integers satisfying (n−1)an+1=(n+1)an−2(n−1)∀n≥1(n-1)a_{n+1}=(n+1)a_n-2(n-1) \forall n\ge 1. If 2000∣a19992000|a_{1999}, find the smallest n≥2n\ge 2 such that 2000∣an2000|a_n.
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