Distribution of quadratic non-residues which are not primitive roots

S. Gun; B. Ramakrishnan; Binod Kumar Sahoo; Ravindranathan Thangadurai

Mathematica Bohemica (2005)

  • Volume: 130, Issue: 4, page 387-396
  • ISSN: 0862-7959

Abstract

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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 2 p h for an odd prime p and h ≥ 1 an integer.

How to cite

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Gun, S., et al. "Distribution of quadratic non-residues which are not primitive roots." Mathematica Bohemica 130.4 (2005): 387-396. <http://eudml.org/doc/249607>.

@article{Gun2005,
abstract = {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.},
author = {Gun, S., Ramakrishnan, B., Sahoo, Binod Kumar, Thangadurai, Ravindranathan},
journal = {Mathematica Bohemica},
keywords = {quadratic non-residues; primitive roots; Fermat numbers; primitive root; Fermat number},
language = {eng},
number = {4},
pages = {387-396},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Distribution of quadratic non-residues which are not primitive roots},
url = {http://eudml.org/doc/249607},
volume = {130},
year = {2005},
}

TY - JOUR
AU - Gun, S.
AU - Ramakrishnan, B.
AU - Sahoo, Binod Kumar
AU - Thangadurai, Ravindranathan
TI - Distribution of quadratic non-residues which are not primitive roots
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 4
SP - 387
EP - 396
AB - 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.
LA - eng
KW - quadratic non-residues; primitive roots; Fermat numbers; primitive root; Fermat number
UR - http://eudml.org/doc/249607
ER -

References

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  1. Über Sequenzen von Potenzresten, Sitzungsberichte Akad. Berlin (1928), 9–16. (German) (1928) 
  2. A necessary and sufficient condition for the primality of Fermat numbers, Math. Bohem. 126 (2001), 541–549. (2001) MR1970256
  3. 10.1090/S0002-9939-1968-0230680-7, Proc. Amer. Math. Soc. 19 (1968), 1169–1170. (1968) Zbl0167.04001MR0230680DOI10.1090/S0002-9939-1968-0230680-7
  4. Primitive roots modulo a prime as consecutive terms of an arithmetic progression, J. Reine Angew. Math. 235 (1969), 185–188. (1969) Zbl0172.32502MR0242759
  5. Arithmetic progressions of primitive roots of a prime II, J. Reine Angew. Math. 244 (1970), 108–111. (1970) Zbl0205.34703MR0266852
  6. 10.1016/0022-314X(71)90046-1, J. Number Theory 3 (1971), 13–18. (1971) Zbl0211.37202MR0285476DOI10.1016/0022-314X(71)90046-1
  7. Arithmetic progressions of primitive roots of a prime III, J. Reine Angew. Math. 256 (1972), 130–137. (1972) Zbl0243.10002MR0308022

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