From: J. Michael Diehl <mdiehl@triton.unm.edu>
Date: Sat, 5 Jun 93 23:30:08 PDT
To: smb@research.att.com
Subject: Re: Dig. Cash Question.
In-Reply-To: <9306052306.AA05980@triton.unm.edu>
Message-ID: <9306060630.AA10639@triton.unm.edu>
MIME-Version: 1.0
Content-Type: text/plain


According to smb@research.att.com:
> 
> 	 If I understand this correctly, if p is not a prime, then n may not be
> 	 unique.
> 
> Well, n isn't unique even if p is prime.  Consider a=10,p=11.
> 10^2=10^4=10^6=10^8=10^10=1 mod 11.  You only get a maximum-length
> cycle if ``a'' is a primitive root, hence the restriction I stated
> in the part I deleted...

That is, if a is a generator of G, or as close to one as possible.  

My thinking was obviously clowded...  Not that I have a beer in me, I remember
that for any element, a of group G, a will have order n, such that n|ord(G).
This implies that there are n different (positive) powers of a which yield a 
particular number, b in our case.  Each of which would qualify as a log.  I
think I understand.

> It doesn't matter that n isn't unique, though you do want a good
> distribution.  Primitive roots have a maximal distribution, which is

Then which root are we to use in discussion?

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