Re: Generators of cyclic group

From: Marcel Martin (mm_at_ellipsa.no.spam.net)
Date: 10/29/03 

Date: Wed, 29 Oct 2003 21:48:50 +0100

Mok-Kong Shen a écrit :
>
> Marcel Martin wrote:
> >
> [snip]
> > In short, if x is a NRQ different from -1, we have (x^2 <> 1) and
> > (x^q <> 1) and (x^(2q) = 1), which implies that x is a generator.
>
> Could you please explain a little bit why this is so?
> Thanks.

If x is in QNR - {-1} then the 3 conditions hold. If they hold, the
order of x is 2q, i.e., the order of x is equal to the group order,
thus x is a generator.

mm

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