# [seqfan] Re: What's the better definition of A001134

Neil Sloane njasloane at gmail.com
Fri May 17 17:33:52 CEST 2013

```For that kind of question, don't forget we have a new "OEIS Help Page" on
the wiki: https://oeis.org/wiki/OEIS_Help_Page

On Fri, May 17, 2013 at 9:01 AM, Emmanuel Vantieghem <
emmanuelvantieghem at gmail.com> wrote:

> Correction : the multiplicative order of  x  modulo  y  is the smallest
> positive number  n  such that  x^n == 1 mod y. Of course, this implies
> that  x^(n-1) !== 1 mod y but it is not suffient..
> _____________________________________
>
> 2013/5/17 David Applegate <david at research.att.com>
>
> > The "history" link on A001134 shows the evolution of the definition:
> >
> > 2 is a quartic residue modulo \$_p\$.
> >
> > Primes p such that 2 is a quartic residue modulo p.
> >
> > Primes p such that 2 is a quartic residue modulo p, but not a
> > higher-order residue. (Don Reble's improvement)
> >
> > Primes p such that the multiplicative order of 2 modulo p is (p-1)/4.
> >
> > If you were asking for an explanation of the definition, rather than the
> > history, the multiplicative order of x modulo y is the n such that
> > x^n === 1 (mod y), but x^(n-1) !== 1 (mod y).
> >
> > -Dave
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
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>

--
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA