Re: prime~.

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

Date: Mon, 4 Oct 2004 02:36:46 -0700

From: mina_world <mina_world@hanmail.net>
Newsgroups: sci.math
Subject: Re: prime~.

>p is a prime.

>show that
>p | (a^p) - 1 for some a in Z
>=> (p^2) | (a^p) - 1

a - 1 = a^p - 1 = 0 (mod p)
a = 1 (mod p)

a = kp + 1
a^p = (kp)^p +..+ p.kp + 1 = 1 (mod p^2)

Exercise:
        p | a^p - b^p ==> p^2 | a^p - b^p 

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