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

From: William Elliot (marsh_at_privacy.net)
Date: 06/10/04 

Date: Thu, 10 Jun 2004 03:43:24 -0700

On Thu, 10 Jun 2004, Ken Oliver wrote:

> "DanKage" <eba012@webmail.uib.no> wrote in message
> > 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.
>
Thanks for a most readable version.
Stuff like
        n^4+4=n^4+4n^2+4-4n^2=(n^2+2)^2-(2n)^2
as others are want to do, requires squinting and deciphering.