# On some equations over finite fields

Ioulia Baoulina^{[1]}

- [1] The Institute of Mathematical Sciences CIT Campus, Taramani Chennai 600113, India

Journal de Théorie des Nombres de Bordeaux (2005)

- Volume: 17, Issue: 1, page 45-50
- ISSN: 1246-7405

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topBaoulina, Ioulia. "On some equations over finite fields." Journal de Théorie des Nombres de Bordeaux 17.1 (2005): 45-50. <http://eudml.org/doc/249448>.

@article{Baoulina2005,

abstract = {In this paper, following L. Carlitz we consider some special equations of $n$ variables over the finite field of $q$ elements. We obtain explicit formulas for the number of solutions of these equations, under a certain restriction on $n$ and $q$.},

affiliation = {The Institute of Mathematical Sciences CIT Campus, Taramani Chennai 600113, India},

author = {Baoulina, Ioulia},

journal = {Journal de Théorie des Nombres de Bordeaux},

keywords = {finite field; Markoff-Hurwitz equation; Gauss sum},

language = {eng},

number = {1},

pages = {45-50},

publisher = {Université Bordeaux 1},

title = {On some equations over finite fields},

url = {http://eudml.org/doc/249448},

volume = {17},

year = {2005},

}

TY - JOUR

AU - Baoulina, Ioulia

TI - On some equations over finite fields

JO - Journal de Théorie des Nombres de Bordeaux

PY - 2005

PB - Université Bordeaux 1

VL - 17

IS - 1

SP - 45

EP - 50

AB - In this paper, following L. Carlitz we consider some special equations of $n$ variables over the finite field of $q$ elements. We obtain explicit formulas for the number of solutions of these equations, under a certain restriction on $n$ and $q$.

LA - eng

KW - finite field; Markoff-Hurwitz equation; Gauss sum

UR - http://eudml.org/doc/249448

ER -

## References

top- I. Baoulina, On the Problem of Explicit Evaluation of the Number of Solutions of the Equation ${a}_{1}^{}{x}_{1}^{2}+\cdots +{a}_{n}^{}{x}_{n}^{2}=b{x}_{1}^{}\cdots {x}_{n}^{}$ in a Finite Field. In Current Trends in Number Theory, Edited by S. D. Adhikari, S. A. Katre and B. Ramakrishnan, Hindustan Book Agency, New Delhi, 2002, 27–37. Zbl1086.11021MR1925639
- A. Baragar, The Markoff Equation and Equations of Hurwitz. Ph. D. Thesis, Brown University, 1991.
- B. C. Berndt, R. J. Evans, K. S. Williams, Gauss and Jacobi Sums. Wiley-Interscience, New York, 1998. Zbl0906.11001MR1625181
- L. Carlitz, Certain special equations in a finite field. Monatsh. Math. 58 (1954), 5–12. Zbl0055.26803MR61121

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