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.

AND:
OR:
NO:

Found problems: 3

2016 Polish MO Finals, 4
Tags: divisibility , order of an element , number theory
Let $k, n$ be odd positve integers greater than $1$. Prove that if there a exists natural number $a$ such that $k|2^a+1, \ n|2^a-1$, then there is no natural number $b$ satisfying $k|2^b-1, \ n|2^b+1$.

2020 Kazakhstan National Olympiad, 3
Tags: number theory , order of an element , prime number
Let $p$ be a prime number and $k,r$ are positive integers such that $p>r$. If $pk+r$ divides $p^p+1$ then prove that $r$ divides $k$.

2017 Turkey EGMO TST, 6
Tags: order of an element , number theory
Find all pairs of prime numbers $(p,q)$, such that $\frac{(2p^2-1)^q+1}{p+q}$ and $\frac{(2q^2-1)^p+1}{p+q}$ are both integers.