Re: proove that n^4 + n is never prime

From: Ken Oliver (ksterling_at_mindspring.com)
Date: 06/10/04 

Date: Thu, 10 Jun 2004 09:47:18 GMT

"DanKage" <eba012@webmail.uib.no> wrote in message
news:nhagc0d64mecpn6edvob9jfe7lnv95kr48@4ax.com...
> Sorry, the statement is that n^4 + 4 is never prime (NOT n^4 + n)
>
>

n^4 + 4 = n^4 +4n^2 + 4 - 4n^2 (add and subtract 4n^2)

            = ( n^2 + 2 )^2 - 4n^2

            = (n^2 + 2 +2n^2) (n^2 + 2 - 2n^2) (Factor as diff of sq's)

So n^4 + 4 is factorable for all n >= 2. Therefore not prime.