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: 2

2009 Hanoi Open Mathematics Competitions, 4
Tags: modular arithmetic , number theory open , number theory
Suppose that $a=2^b$, where $b=2^{10n+1}$. Prove that $a$ is divisible by 23 for any positive integer $n$

2013 European Mathematical Cup, 2
Tags: induction , number theory open , number theory
Palindrome is a sequence of digits which doesn't change if we reverse the order of its digits. Prove that a sequence $(x_n)^{\infty}_{n=0}$ defined as $x_n=2013+317n$ contains infinitely many numbers with their decimal expansions being palindromes.