2013 OIM Problems/Problem 3

Problem

Let $A = \left\{1, 2, 3, \cdots , n\right\}$ with $n > 5$ . Prove that there exists a finite set $B$ of distinct positive integers such that $A \subseteq B$ and has the property

$\prod_{x \in B}^{}x=\sum_{x \in B}^{}x^2$

That is, the product of the elements of B is equal to the sum of the squares of the elements of B.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

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2013 OIM Problems/Problem 3

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