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International Contests
Austrian-Polish
1983 Austrian-Polish Competition
4
4
Part of
1983 Austrian-Polish Competition
Problems
(1)
a, b, a + b either all belong to A or all belong to B where A,B partitions of N
Source: Austrian Polish 1983 APMC
4/30/2020
The set
N
N
N
has been partitioned into two sets A and
B
B
B
. Show that for every
n
ā
N
n \in N
n
ā
N
there exist distinct integers
a
,
b
>
n
a, b > n
a
,
b
>
n
such that
a
,
b
,
a
+
b
a, b, a + b
a
,
b
,
a
+
b
either all belong to
A
A
A
or all belong to
B
B
B
.
number theory
positive integers
Sets
partition