Problem 536

Erdős Problem #536: declared status 'open'. Formalized: yes. Let $\epsilon>0$ and $N$ be sufficiently large. Is it true that if $A\subseteq \{1,\ldots,N\}$ has size at least $\epsilon N$ then there must be distinct $a,b,c\in A$ such that$$[a,b]=[b,c]=[a,c],$$where $[a,b]$ denotes the least common multiple? Prize: no. Tags: number theory.