MathDB
Problems
Contests
International Contests
Austrian-Polish
1978 Austrian-Polish Competition
4
4
Part of
1978 Austrian-Polish Competition
Problems
(1)
Partition of N avoiding ratio c
Source: Austrian-Polish 1978, Problem 4
7/5/2015
Let
c
≠
1
c\neq 1
c
=
1
be a positive rational number. Show that it is possible to partition
N
\mathbb{N}
N
, the set of positive integers, into two disjoint nonempty subsets
A
,
B
A,B
A
,
B
so that
x
/
y
≠
c
x/y\neq c
x
/
y
=
c
holds whenever
x
x
x
and
y
y
y
lie both in
A
A
A
or both in
B
B
B
.
ratio
algebra
combinatorics