Problem Statement
What is the size of the largest $A\subseteq \{1,\ldots,n\}$ such that if $a\leq b\leq c\leq d\in A$ are such that $abcd$ is a square then $ad=bc$?
Categories:
Number Theory Squares
Progress
A question of Erdős, Sárközy, and Sós. Erdős claims that Sárközy proved that $\lvert A\rvert =o(n)$. The primes show that $\lvert A\rvert \gg n/\log n$ is possible.See also [121].
Source: erdosproblems.com/888 | Last verified: January 19, 2026