Question 4
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 $(m, n)$.
Proposed by Rishabh Das. One nonofficial editorial point; manual essay grading.
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 $(m, n)$.
Proposed by Rishabh Das. One nonofficial editorial point; manual essay grading.