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

From: Ignacio Larrosa Cañestro (ilarrosaQUITARMAYUSCULAS_at_mundo-r.com)
Date: 06/10/04 

Date: Thu, 10 Jun 2004 12:30:04 +0200

Ken Oliver <ksterling@mindspring.com> escribió en el mensaje
 news:G6Wxc.4674$Y3.2356@newsread2.news.atl.earthlink.net:

> "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.

You meant

> = (n^2 + 2 +2n) (n^2 + 2 - 2n) 

-- 
Best regards,
Ignacio Larrosa Cañestro
A Coruña (España)
ilarrosaQUITARMAYUSCULAS@mundo-r.com
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