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2013 IberoAmerican
3
3
Part of
2013 IberoAmerican
Problems
(1)
Product equals sum of squares
Source: 28th Iberoamerican Olympiad 2013, Problem 3
9/24/2013
Let
A
=
{
1
,
.
.
.
,
n
}
A = \{1,...,n\}
A
=
{
1
,
...
,
n
}
with n \textgreater 5. Prove that one can find
B
B
B
a finite set of positive integers such that
A
A
A
is a subset of
B
B
B
and
∑
x
∈
B
x
2
=
∏
x
∈
B
x
\displaystyle\sum_{x \in B} x^2 = \displaystyle\prod_{x \in B} x
x
∈
B
∑
x
2
=
x
∈
B
∏
x
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