Number theory · Remainders · Divisibility rules · Coprime moduli · Repeated digit numbers
Let \(N\) be the number whose decimal expansion consists of \(2025\) copies of the digit \(3\):
\[ N = \underbrace{33\ldots3}_{2025} . \]
What remainder does \(N\) leave when it is divided by \(12\)?
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
- E \(9\)
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2025, 1. letnik, category A, problem A2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source