In this paper, we obtain a su$cient condition for the diagonal equation to have only the trivial solution over "nite "elds. This result improves a theorem of Sun (J. Sichuan Normal ;niv. Nat. Sci. Ed. 26 (1989), 55}59) greatly and proves that the conjecture posed by Powell (J. Number ΒΉheory 18 (1984
On Diagonal Equations over Finite Fields
β Scribed by Sun Qi
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 170 KB
- Volume
- 3
- Category
- Article
- ISSN
- 1071-5797
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β¦ Synopsis
We get an explicit formula for the number of solutions of a diagonal equation over finite fields, under a certain natural restriction on the exponents.
π SIMILAR VOLUMES
In this paper, we give a reduction theorem for the number of solutions of any diagonal equation over a finite field. Using this reduction theorem and the theory of quadratic equations over a finite field, we also get an explicit formula for the number of solutions of a diagonal equation over a finit
By using results of coding theory, we give results on the number of solutions of some systems of diagonal equations over finite fields.
X generalization of a theorem of A. D. PORTER on the number of solutions of the k-linear equation 2 ai n x , ~ = a over a finite field is given.