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a copsychus and a sparrow, move across edges of a regular polygon

Source: Mathley 2014.3 p1

August 18, 2020
combinatorics

Problem Statement

A copsychus and a sparrow, each initially located at one of the vertex of a regular polygon with 103103 edges, fly clockwise to another vertex each. The copsychus moves across ℓ\ell edges each time while the sparrow moves throughd d edges of the polygon, where ℓ≠d\ell \ne d are both integers less than 103103. Assume that, during their journeys, the copsychus has stopped at mm vertices while sparrow has stopped at nn vertices of the polygon, for m≥n≥3m \ge n \ge 3. Determine the value of m,nm, n given that there is only one common single vertex of the polygon that both of birds have stopped at, and there is only one vertex that neither of the birds have reached.
Vu Thi Khoi, Topo University, Hanoi Mathematics Institute, Vietnam, Hoang Qu6c Vietnam, Hanoi.
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