IMC 2024 · Problem 3

Day 131st IMC · Blagoevgrad, Bulgaria

Statement

For which positive integers $n$ does there exist an $n \times n$ matrix $A$ whose entries are all in $\{0, 1\}$ , such that $A^2$ is the matrix of all ones?

Official solution

Hidden so you can work on the problem first.

Proposed by Alex Avdiushenko, Neapolis University Paphos, Cyprus.