Problem

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

Tags: modular arithmetic, number theory, greatest common divisor, number theory proposed



Find all Arithmetic progressions $a_{1},a_{2},...$ of natural numbers for which there exists natural number $N>1$ such that for every $k\in \mathbb{N}$: $a_{1}a_{2}...a_{k}\mid a_{N+1}a_{N+2}...a_{N+k}$