| Title:
|
Distribution of quadratic non-residues which are not primitive roots (English) |
| Author:
|
Gun, S. |
| Author:
|
Ramakrishnan, B. |
| Author:
|
Sahu, B. |
| Author:
|
Thangadurai, R. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
130 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
387-396 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
quadratic non-residues |
| Keyword:
|
primitive roots |
| Keyword:
|
Fermat numbers |
| MSC:
|
11A07 |
| MSC:
|
11A15 |
| MSC:
|
11N69 |
| idZBL:
|
Zbl 1105.11034 |
| idMR:
|
MR2182384 |
| DOI:
|
10.21136/MB.2005.134213 |
| . |
| Date available:
|
2009-09-24T22:22:37Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134213 |
| . |
| Reference:
|
[1] A. Brauer: Über Sequenzen von Potenzresten.Sitzungsberichte Akad. Berlin (1928), 9–16. (German) |
| Reference:
|
[2] M. Křížek, L. Somer: A necessary and sufficient condition for the primality of Fermat numbers.Math. Bohem. 126 (2001), 541–549. MR 1970256 |
| Reference:
|
[3] E. Vegh: Pairs of consecutive primitive roots modulo a prime.Proc. Amer. Math. Soc. 19 (1968), 1169–1170. Zbl 0167.04001, MR 0230680, 10.1090/S0002-9939-1968-0230680-7 |
| Reference:
|
[4] E. Vegh: Primitive roots modulo a prime as consecutive terms of an arithmetic progression.J. Reine Angew. Math. 235 (1969), 185–188. Zbl 0172.32502, MR 0242759 |
| Reference:
|
[5] E. Vegh: Arithmetic progressions of primitive roots of a prime II.J. Reine Angew. Math. 244 (1970), 108–111. Zbl 0205.34703, MR 0266852 |
| Reference:
|
[6] E. Vegh: A note on the distribution of the primitive roots of a prime.J. Number Theory 3 (1971), 13–18. Zbl 0211.37202, MR 0285476, 10.1016/0022-314X(71)90046-1 |
| Reference:
|
[7] E. Vegh: Arithmetic progressions of primitive roots of a prime III.J. Reine Angew. Math. 256 (1972), 130–137. Zbl 0243.10002, MR 0308022 |
| . |
