Errors in Bignum arithmetic?
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Date:  20100810 (13:40) 
From:  Jim Pryor <lists+caml@j...> 
Subject:  Re: [Camllist] Errors in Bignum arithmetic? 
On Tue, Aug 10, 2010 at 08:46:49AM 0400, David House wrote: > > You've missed a small detail in the definition here. n is Carmichael > iff a^(n1) = 1 (mod n) for all a with gcd(a,n) = 1; in other words, > you are only allowed to consider a's which are coprime to your > supposed Carmichael number. > On Tue, Aug 10, 2010 at 02:52:19PM +0200, Ronan Le Hy wrote: > Hello, > > 2010/8/10 Jim Pryor <lists+caml@jimpryor.net>: > > Fermat's Little Theorem says that when p is prime, then for all 1<=a<p, > > a**(p1) mod p = 1. [...] > > > > The Carmichael numbers are a series of composites that have the property > > for all choices of a. http://mathworld.wolfram.com/CarmichaelNumber.html > > This page says "for every choice of a [...] where a and p are > relatively prime". I believe that explains that your examples below do > not work : Excellent, I thought the error was most likely my own. Thanks for identifying it so quickly.  Jim Pryor profjim@jimpryor.net