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Found problems: 1

2024 USAMO, 4
Tags: USAMO 2024 , combinatorics
Let $m$ and $n$ be positive integers. A circular necklace contains $mn$ beads, each either red or blue. It turned out that no matter how the necklace was cut into $m$ blocks of $n$ consecutive beads, each block had a distinct number of red beads. Determine, with proof, all possible values of the ordered pair $(m, n)$. [i]Proposed by Rishabh Das[/i]