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Errors in Bignum arithmetic?
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 Date: 2010-08-10 (13:40) From: Jim Pryor Subject: Re: [Caml-list] 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^(n-1) = 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**(p-1) 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

```