IN-TST 2002 Problem 12

Let $a,b$ be integers with $0<a<b$ . A set $\{x,y,z\}$ of non-negative integers is olympic if $x<y<z$ and if $\{z-y,y-x\}=\{a,b\}$ . Show that the set of all non-negative integers is the union of pairwise disjoint olympic sets.