Problem

Source: Iranian TST 2018, second exam, day1, problem 3

Tags: number theory



Let $a_1,a_2,a_3,\cdots $ be an infinite sequence of distinct integers. Prove that there are infinitely many primes $p$ that distinct positive integers $i,j,k$ can be found such that $p\mid a_ia_ja_k-1$. Proposed by Mohsen Jamali