Higher-order residue ?

Don Reble djr at nk.ca
Sun Jul 9 13:23:38 CEST 2006

> A001133
> Primes p such that 2 is a cubic residue modulo p, but not a
> higher-order residue.
> 43,109,157,...
> and similarly sequences A001136, A115591, A001134, A001135.

> So 2 is indeed a cubic residue mod 43, since 20^3=2 (mod 43).
> But ... it is also a 5-th residue, since 8^5=2 (mod 43)
> and also a 9-th residue, since 26^9=2 (mod 43) and so on...

    Oops, I reworded those badly.

    A001133 is the set of primes P, such that 2 generates 1/3 of the
    multiplicative group modulo P. And for each of the other sequences,
    2 generates a particular fraction of P's group.

Don Reble  djr at nk.ca

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