Let $ϵ>0$ and $N$ be sufficiently large. If $A\subseteq \{1,\dots ,N\}$ has $|A|\ge ϵN$ then must there exist $a_1,a_2,a_3\in A$ and distinct primes $p_1,p_2,p_3$ such that$$a_1{p}_1=a_2{p}_2=a_3{p}_3?$$