MathDB

Let

p{}

and

q{}

be two coprime positive integers. A frog hops along the integer line so that on every hop it moves either

p{}

units to the right or

q{}

units to the left. Eventually, the frog returns to the initial point. Prove that for every positive integer

d{}

with

d < p + q

there are two numbers visited by the frog which differ just by

d{}

.
Nikolay Belukhov

Problem Statement