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On the solution of algebraic equations over finite fields

✍ 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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On Diagonal Equations over Finite Fields
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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.

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✍ Alexandra Shlapentokh πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 825 KB

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