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: 2

2013 Czech-Polish-Slovak Junior Match, 1
Decide whether there are infinitely many primes $p$ having a multiple in the form $n^2 + n + 1$ for some natural number $n$
infinitely many prime number theory prime numbers

2018 Danube Mathematical Competition, 2
Prove that there are in finitely many pairs of positive integers $(m, n)$ such that simultaneously $m$ divides $n^2 + 1$ and $n$ divides $m^2 + 1$.
divisor infinitely many number theory