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        riddles >> easy >> n^4 + 4
        
(Message started by: NickH on Jan 25th, 2003, 4:18pm)
Title: n^4 + 4
Post by NickH on Jan 25th, 2003, 4:18pm
An easy one...

Show that, for integers n > 1, n4 + 4 is never prime.
Title: Re: n^4 + 4
Post by BNC on Jan 26th, 2003, 1:03am
[hide]
n^4+4=
(n^2)^2+2^2=
(n^2+2)^2-2*2*n^2=
(n^2+2)^2-4n^2=
[(n^2+2)+2n]*[(n^2+2)-2n]=
(n^2+2n+2)*(n^2-2n+2)

n^2+2n+2 > 1 for n>1
n^2-2n+2 > 1 for n>1

QED
[/hide]


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