Problem

Source: Iran 2024 3rd round number theory exam p2

Tags: number theory



For all positive integers $n$ Prove that one can find pairwise coprime integers $a,b,c>n$ such that the set of prime divisors of the numbers $a+b+c$ and $ab+bc+ac$ coincides. Proposed by Mohsen Jamali and Hesam Rajabzadeh