2001 IMO Shortlist S08

A set of three nonnegative integers $\{x,y,z\}$ with $x < y < z$ is called *historic* if $\{z-y,y-x\} = \{1776,2001\}$ . Show that the set of all nonnegative integers can be written as the union of pairwise disjoint historic sets.

如果 $\{z-y,y-x\} = \{1776,2001\}$ ，则三个非负整数 $\{x,y,z\}$ 且 $x < y < z$ 的集合称为*历史*。证明所有非负整数的集合可以写成成对不相交历史集合的并集。