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: 8

2014 France Team Selection Test, 3
Tags: number theory , prime divisor , polynomial , IMO Shortlist , imo shortlist n3 , Hi
Prove that there exist infinitely many positive integers $n$ such that the largest prime divisor of $n^4 + n^2 + 1$ is equal to the largest prime divisor of $(n+1)^4 + (n+1)^2 +1$.

2014 Belarus Team Selection Test, 3
Tags: number theory , prime divisor , polynomial , IMO Shortlist , imo shortlist n3 , Hi
Prove that there exist infinitely many positive integers $n$ such that the largest prime divisor of $n^4 + n^2 + 1$ is equal to the largest prime divisor of $(n+1)^4 + (n+1)^2 +1$.

2013 IMO Shortlist, N3
Tags: number theory , prime divisor , polynomial , IMO Shortlist , imo shortlist n3 , Hi
Prove that there exist infinitely many positive integers $n$ such that the largest prime divisor of $n^4 + n^2 + 1$ is equal to the largest prime divisor of $(n+1)^4 + (n+1)^2 +1$.

2014 France Team Selection Test, 3
Tags: number theory , prime divisor , polynomial , IMO Shortlist , imo shortlist n3 , Hi
Prove that there exist infinitely many positive integers $n$ such that the largest prime divisor of $n^4 + n^2 + 1$ is equal to the largest prime divisor of $(n+1)^4 + (n+1)^2 +1$.

2014 Brazil Team Selection Test, 2
Tags: number theory , prime divisor , polynomial , IMO Shortlist , imo shortlist n3 , Hi
Prove that there exist infinitely many positive integers $n$ such that the largest prime divisor of $n^4 + n^2 + 1$ is equal to the largest prime divisor of $(n+1)^4 + (n+1)^2 +1$.

2014 Taiwan TST Round 1, 5
Tags: number theory , prime divisor , polynomial , IMO Shortlist , imo shortlist n3 , Hi
Prove that there exist infinitely many positive integers $n$ such that the largest prime divisor of $n^4 + n^2 + 1$ is equal to the largest prime divisor of $(n+1)^4 + (n+1)^2 +1$.

2014 Contests, 3
Tags: number theory , prime divisor , polynomial , IMO Shortlist , imo shortlist n3 , Hi
Prove that there exist infinitely many positive integers $n$ such that the largest prime divisor of $n^4 + n^2 + 1$ is equal to the largest prime divisor of $(n+1)^4 + (n+1)^2 +1$.

Russian TST 2014, P2
Tags: number theory , prime divisor , polynomial , IMO Shortlist , imo shortlist n3 , Hi
Prove that there exist infinitely many positive integers $n$ such that the largest prime divisor of $n^4 + n^2 + 1$ is equal to the largest prime divisor of $(n+1)^4 + (n+1)^2 +1$.