This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 52

2004 Switzerland - Final Round, 6
Tags: number theory , last digit
Determine all $k$ for which there exists a natural number n such that $1^n + 2^n + 3^n + 4^n$ with exactly $k$ zeros at the end.

2013 Saudi Arabia Pre-TST, 2.3
Tags: number theory , power , last digit
The positive integer $a$ is relatively prime with $10$. Prove that for any positive integer $n$, there exists a power of $a$ whose last $n$ digits are $\underbrace{0...0}_\text{n-1}1$.