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: 128

1976 IMO Shortlist, 11
Tags: number theory , digit , decimal representation , exponential
Prove that $5^n$ has a block of $1976$ consecutive $0's$ in its decimal representation.

2019 India PRMO, 7
Tags: algebra , number theory , decimal representation
Let $s(n)$ denote the sum of digits of a positive integer $n$ in base $10$. If $s(m)=20$ and $s(33m)=120$, what is the value of $s(3m)$?

1984 Spain Mathematical Olympiad, 7
Tags: digit , number theory , decimal representation
Consider the natural numbers written in the decimal system. (a) Find the smallest number which decreases five times when its first digit is erased. Which form do all numbers with this property have? (b) Prove that there is no number that decreases $12$ times when its first digit is erased. (c) Find the necessary and sufficient condition on $k$ for the existence of a natural number which is divided by $k$ when its first digit is erased.