Find all sets S of positive integers that satisfy all of the following.1. If a,b are two not necessarily distinct elements in S, then gcd(a,b), ab are also in S.
2. If m,n are two positive integers with n∤m, then there exists an element s in S such that m2∣s and n2∤s.
3. For any odd prime p, the set formed by moduloing all elements in S by p has size exactly 2p+1. number theorygreatest common divisorSets