ITOT 42 Spring 2021 - THCS A - additive practice Question 7

Let $p,q$ be coprime positive integers. A frog starts at 0 on the integer line and makes a nonempty sequence of hops, each either $p$ units right or $q$ units left, eventually returning to 0. Prove that for every positive integer $d<p+q$, two positions visited by the frog differ by exactly $d$. (12 points)



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