Question 63
Let $D$ be a non-empty set of positive integers, let $d$ be the greatest common divisor of $D$, and let $d\mathbb{Z} = \{dn : n \in \mathbb{Z}\}$. Prove that there exists a bijection $f: \mathbb{Z} \to d\mathbb{Z}$ such that $|f(n) - f(n-1)|$ is a member of $D$ for all integers $n$.
*Amer. Math. Monthly*
*Amer. Math. Monthly*