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beads on a necklace

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March 21, 2024

Problem Statement

Let mm and nn be positive integers. A circular necklace contains mnmn beads, each either red or blue. It turned out that no matter how the necklace was cut into mm blocks of nn consecutive beads, each block had a distinct number of red beads. Determine, with proof, all possible values of the ordered pair (m,n)(m, n).
Proposed by Rishabh Das
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