Number theory · Irrationality · Perfect squares · Squarefree integers · Prime factorisation
Prove that there are no natural numbers \(a\) and \(b\) satisfying
\[ \sqrt{a} + \sqrt{b} = \sqrt{2021} . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2021, 1. letnik, category A, problem B1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source