IN-TST 2009 Problem 11

Find all integers $n\ge 2$ with the following property:

There exists three distinct primes $p,q,r$ such that whenever $a_1,a_2,a_3,\cdots,a_n$ are $n$ distinct positive integers with the property that at least one of $p,q,r$ divides $a_j - a_k \ \forall 1\le j\le k\le n$ , one of $p,q,r$ divides all of these differences.