MathDB

Partition of N avoiding ratio c

Source: Austrian-Polish 1978, Problem 4

July 5, 2015

ratioalgebracombinatorics

Problem Statement

Let

c\neq 1

be a positive rational number. Show that it is possible to partition

\mathbb{N}

, the set of positive integers, into two disjoint nonempty subsets

A,B

so that

x/y\neq c

holds whenever

x

and

y

lie both in

A

or both in

B