Number theory · Divisibility · Repdigits · Digit sum · Decimal representation
Find the smallest natural number \(n\) for which the sum
\[ n + 2n + 3n + \cdots + 9n \]
is a number whose decimal representation has all of its digits equal.
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2005, 1. letnik, category A, problem 1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source