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Product equals sum of squares

Source: 28th Iberoamerican Olympiad 2013, Problem 3

September 24, 2013

inductionnumber theory proposednumber theoryIberoamerican

Problem Statement

Let

A = \{1,...,n\}

with n \textgreater 5. Prove that one can find

B

a finite set of positive integers such that

A

is a subset of

B

and

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