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