# Math Help - Prime number 2

1. ## Prime number 2

Hi,

How to show $(\forall n \in \mathbb{N}*) (2^{2n}+5)$ isn't a positive prime nimber????

2. Originally Posted by bhitroofen01
Hi,

How to show $(\forall n \in \mathbb{N}*) (2^{2n}+5)$ isn't a positive prime nimber????

$2^2=4=1\!\!\!\pmod 3\Longrightarrow 2^{2n}=(2^2)^n=1\!\!\!\pmod n$ , and since $5=2\!\!\!\pmod 3$ , we get $2^{2n}+5=1+2=0\!\!\!\pmod 3$

Tonio