Number theory · Nested radicals · Perfect powers · Prime factorization · Minimization
Let \(a\) and \(b\) be natural numbers, both greater than \(1\), such that
\[ \sqrt{a\sqrt{a\sqrt{a}}} = b . \]
What is the smallest possible value of the sum \(a + b\)?
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2003, 1. letnik, category A, problem 5. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source