Re: how to factor a^n - b^n
- From: Phil Carmody <thefatphil_demunged@xxxxxxxxxxx>
- Date: 26 Nov 2005 20:35:54 +0200
"Kenneth Bull" <kenneth.bull@xxxxxxxxx> writes:
> How does one factor a^n - b^n where n is a natural number?
Firstly there are the simple cyclotomic factors.
Taking Phi(n,a,b) as the homogenous n-th cyclotomic polynomial in a and b,
Phi(d,a,b) | a^n-b^n for all d|n.
In addition, there may be Aurefeuillian factorisations of those
cyclotomic terms. They exist when a and b have a particular relation
to n. Brent documents many of these relations in some paper with
a darned obvious name that I forget, and it's also in Riesel's PNaCMfF.
Phil
--
If a religion is defined to be a system of ideas that contains unprovable
statements, then Godel taught us that mathematics is not only a religion, it
is the only religion that can prove itself to be one. -- John Barrow
.
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