On some equations over finite fields
Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 1, pp. 45-50.

Dans ce papier, suivant L. Carlitz, nous considérons des équations particulières à n variables sur le corps fini à q éléments. Nous obtenons des formules explicites pour le nombre de solutions de ces équations, sous une certaine condition sur n et q.

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.

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     author = {Ioulia Baoulina},
     title = {On some equations over finite fields},
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Ioulia Baoulina. On some equations over finite fields. Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 1, pp. 45-50. doi : 10.5802/jtnb.475. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.475/

[1] I. Baoulina, On the Problem of Explicit Evaluation of the Number of Solutions of the Equation a 1 x 1 2 ++a n x n 2 =bx 1 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. | MR 1925639 | Zbl 01936544

[2] A. Baragar, The Markoff Equation and Equations of Hurwitz. Ph. D. Thesis, Brown University, 1991.

[3] B. C. Berndt, R. J. Evans, K. S. Williams, Gauss and Jacobi Sums. Wiley-Interscience, New York, 1998. | MR 1625181 | Zbl 0906.11001

[4] L. Carlitz, Certain special equations in a finite field. Monatsh. Math. 58 (1954), 5–12. | MR 61121 | Zbl 0055.26803

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