Number theory · Trailing zeros · Modular arithmetic · Powers
Let
\[ N = 1^{n} + 2^{n} + 3^{n} + 4^{n}, \qquad n \in \mathbb{N}. \]
What is the greatest number of zeros in which the number \(N\) can end?
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Serbian Municipal Competition 2024, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source