2013 OIM Problems/Problem 3
Problem
Let 
with 
. Prove that there exists a finite set 
of distinct positive integers such that 
and has the property
![\[\prod_{x \in B}^{}x=\sum_{x \in B}^{}x^2\]](http://latex.artofproblemsolving.com/f/e/e/feef08840dbe59d14f789a3c66b7bca851c17581.png)
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
Solution
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