Expressing n as a+b from the infinite sets A and B
Source: Baltic Way 1997
January 28, 2011
combinatorics proposedcombinatorics
Problem Statement
a) Prove the existence of two infinite sets and , not necessarily disjoint, of non-negative integers such that each non-negative integer is uniquely representable in the form with .
b) Prove that for each such pair , either or contains only multiples of some integer .