Re: Counterexample to t( (c^n - a^n) mod b ) | phi(b)
From: Daniel W. Johnson (panoptes_at_iquest.net)
Date: 11/19/04
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Date: Fri, 19 Nov 2004 14:12:50 -0500
Doug Goncz <dgoncz@aol.com> blithered:
> >From: Phil Carmody thefatphil_demunged@yahoo.co.uk
>
> >Don't just "say", prove.
>
> Good advice.
>
> a b c (c^n - a^n) mod b
> 5 6 7 0 2 0 2 0 2...
>
> period is two (2).
>
> The totatives of b=6 are 1, 4, and 5. 1 has no factor and can have no
> factor in common with 6. phi(6) = 3.
gcd(4,6) = 2 > 1. 4 is not a totative of 6.
So, what is 5^phi(6) mod 6 ?
-- Daniel W. Johnson panoptes@iquest.net http://members.iquest.net/~panoptes/ 039 53 36 N / 086 11 55 W
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