ISL 2001 C4

Difficulty band 6

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.

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