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product of all integers of form i^3+1 is a perfect square

Source: Balkan MO ShortList 2009 N3

April 6, 2020
number theory

Problem Statement

Determine all integers 1m,1n20091 \le m, 1 \le n \le 2009, for which \begin{align*} \prod_{i=1}^n \left( i^3 +1 \right) = m^2 \end{align*}