Number theory · Prime factorization · Perfect powers · Divisibility · Exponents
Find the smallest natural number \(n\) that is divisible by \(20\) and for which \(n^2\) is a perfect cube and \(n^3\) is a perfect square.
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2009, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source