Re: Counterexample to t( (c^n - a^n) mod b ) | phi(b)

From: Doug Goncz (dgoncz_at_aol.com)
Date: 11/19/04 

Date: 19 Nov 2004 12:06:16 GMT

>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.

The period of the dual subtractive exponential generator with gcd(a,b,c)=1 and
a<b<c<a+b

(c^n - a^n) mod b

does not always divide the phi of its corresponding base.

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