Number theory · Digit sums · Divisibility · Modular arithmetic
Is there a natural number \(n\) with the following property: if \(n\) is multiplied by the sum of its own digits, then the digits of the resulting product add up to \(3\)?
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2004, 1. letnik, category A, problem 1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source