MathDB
Putnam 1999 B6

Source:

December 22, 2012
Putnamnumber theoryleast common multiplerelatively primeprime numberscollege contestsPutnam number theory

Problem Statement

Let SS be a finite set of integers, each greater than 11. Suppose that for each integer nn there is some s∈Ss\in S such that gcd⁡(s,n)=1\gcd(s,n)=1 or gcd⁡(s,n)=s\gcd(s,n)=s. Show that there exist s,t∈Ss,t\in S such that gcd⁡(s,t)\gcd(s,t) is prime.
Back to ProblemsView on AoPS