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

Emmanuel Vantieghem emmanuelvantieghem at gmail.com
Fri May 17 15:01:37 CEST 2013

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
>
>
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