Saturday, 22 August 2015

number theory - A must contain two relatively prime elements




Let A be a set of positive integers such that no positive integer greater than 1 divides all the elements of A. Prove or disprove that A must contain two relatively prime elements.




This seems to be true, but I wasn't sure how to prove it. Maybe we can prove it by a proof by contradiction?


Answer



{6,10,15} is a counterexample, or more generally {p1p2,p1p3,p2p3} for any primes p1,p2,p3.


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