Question 57
Find all integers $n \ge 2$ and all primes $p, q, r$ with the property: whenever distinct positive integers $a_1, a_2, \dots, a_n$ are such that the difference $a_j - a_k$, $1 \le j \lt k \le n$ is divisible by at least one of $p, q, r$ implies that one of $p, q, r$ divides all the differences $a_j - a_k$, $1 \le j \lt k \le n$.