1
$\begingroup$

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?

$\endgroup$
0
7
$\begingroup$

$\{6,10,15\}$ is a counterexample, or more generally $\{p_1p_2,p_1p_3,p_2p_3\}$ for any primes $p_1,p_2,p_3$.

$\endgroup$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.