On the solution of algebraic equations over finite fields
β Scribed by E.R. Berlekamp; H. Rumsey; G. Solomon
- Book ID
- 114036625
- Publisher
- Elsevier Science
- Year
- 1967
- Weight
- 512 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0019-9958
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π 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 ΒΉheory 18 (1984
We show that Diophantine problem (otherwise known as Hilbert's Tenth Problem) is undecidable over the fields of algebraic functions over the finite fields of constants of characteristic greater than two. This is the first example of Diophantine undecidability over any algebraic field. We also show t