Problem 724

Erdős Problem #724: declared status 'open'. Formalized: no. Let $f(n)$ be the maximum number of mutually orthogonal Latin squares of order $n$. Is it true that$$f(n) \gg n^{1/2}?$$ Current best: Euler conjectured that $f(n)=1$ when $n\equiv 2\pmod{4}$, but this was disproved by Bose, Parker, and Shrikhande [BPS60] who proved $f(n)\geq 2$ for $n\geq 7$. Prize: no. OEIS: A001438. Tags: combinatorics.