Article
Keywords:
quadratic non-residues; primitive roots; Fermat numbers
Summary:
In this article we study, using elementary and combinatorial methods, the distribution of quadratic non-residues which are not primitive roots modulo $p^h$ or $2p^h$ for an odd prime $p$ and $h\ge 1$ an integer.
References:
[1] A. Brauer: Über Sequenzen von Potenzresten. Sitzungsberichte Akad. Berlin (1928), 9–16. (German)
[2] M. Křížek, L. Somer:
A necessary and sufficient condition for the primality of Fermat numbers. Math. Bohem. 126 (2001), 541–549.
MR 1970256
[4] E. Vegh:
Primitive roots modulo a prime as consecutive terms of an arithmetic progression. J. Reine Angew. Math. 235 (1969), 185–188.
MR 0242759 |
Zbl 0172.32502
[5] E. Vegh:
Arithmetic progressions of primitive roots of a prime II. J. Reine Angew. Math. 244 (1970), 108–111.
MR 0266852 |
Zbl 0205.34703
[7] E. Vegh:
Arithmetic progressions of primitive roots of a prime III. J. Reine Angew. Math. 256 (1972), 130–137.
MR 0308022 |
Zbl 0243.10002