Number theory · Divisibility rules · Powers of ten · Factorisation of sums of powers · Prime factorisation
Let \(n\) be the number \(100\ldots001\) whose decimal expansion consists of the digit \(1\), then \(2017\) digits \(0\), then the digit \(1\) again.
Decide, with proof, whether \(n\) is divisible by
(a) \(11\); (b) \(101\); (c) \(1001\).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), odbirno (qualifying) round 2017, 1. letnik, category A, problem 1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source