Number theory · Divisors · Bounding arguments · Exhaustive case check · Equality case
Find all natural numbers \(n\) whose cube equals the sum of the squares of three divisors of \(n\), where the three divisors need not be different from one another.
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2019, 1. letnik, category A, problem B1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source