Simultaneous diagonal equations over certain p-adic fields
✍ Scribed by Eberhard Dörner
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 432 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0022-314X
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📜 SIMILAR VOLUMES
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.
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 ¹heory 18 (1984
By using results of coding theory, we give results on the number of solutions of some systems of diagonal equations over finite fields.