This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2005 China Team Selection Test, 3
Tags: modular arithmetic , binomial expansion , fermat number , power of 2 , number theory
$n$ is a positive integer, $F_n=2^{2^{n}}+1$. Prove that for $n \geq 3$, there exists a prime factor of $F_n$ which is larger than $2^{n+2}(n+1)$.

2005 China Team Selection Test, 3
Tags: number theory , modular arithmetic , binomial expansion , fermat number , power of 2
$n$ is a positive integer, $F_n=2^{2^{n}}+1$. Prove that for $n \geq 3$, there exists a prime factor of $F_n$ which is larger than $2^{n+2}(n+1)$.