# Prime number 2

• May 1st 2010, 04:58 AM
bhitroofen01
Prime number 2
Hi,

How to show $(\forall n \in \mathbb{N}*) (2^{2n}+5)$ isn't a positive prime nimber????
• May 1st 2010, 05:03 AM
tonio
Quote:

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