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Rioplatense Mathematical Olympiad, Level 3
1998 Rioplatense Mathematical Olympiad, Level 3
3
3
Part of
1998 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
e \in B, e divides an odd number of elements of B, iff e \in A
Source: Rioplatense 1998 L3 P3
9/19/2022
Let
X
X
X
be a finite set of positive integers. Prove that for every subset
A
A
A
of
X
X
X
, there is a subset
B
B
B
of
X
X
X
, with the following property: For each element
e
e
e
of
X
X
X
,
e
e
e
divides an odd number of elements of
B
B
B
, if and only if
e
e
e
is an element of
A
A
A
.
number theory
divides