From: Severian <severian@matachin.fsnet.co.uk>
Subject: Re: primes: irregular vs regular
Date: Sun, 11 Jun 2000 09:42:08 +0100
Newsgroups: sci.math
Summary: [missing]

Manning wrote:
> 
> Could someone explain to me the difference between a regular and an
> irregular prime? I know that 37, 59 and 67 are the irregulars below 100,
> but I can't see what distinguishes them from all of the others.

The prime p is regular if p does not divide the class number of
the p-th cyclotomic field Q(exp(2 pi i/p)). Kummer proved that if
p is a regular prime then there are no nonzero integers a, b and c
with a^p + b^p + c^p = 0.

-- 
Severian
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