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Find all Arithmetic progressions

Source: Iran TST 2013:TST 2,Day 1,Problem 2

April 23, 2013

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Problem Statement

Find all Arithmetic progressions

a_{1},a_{2},...

of natural numbers for which there exists natural number

N>1

such that for every

k\in \mathbb{N}

a_{1}a_{2}...a_{k}\mid a_{N+1}a_{N+2}...a_{N+k}