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 combinatoricsCombinatorial Number TheoryTournament of TownsKvant