MathDB

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

4