Number theory · Decimal representation · Divisibility · Digits
Find every natural number \(n \ge 10\) all of whose decimal digits are nonzero and which has the following property: deleting any single digit of \(n\) leaves a number that divides \(n\).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2012, 1. letnik, category A, problem 1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source