Special equations in a finite field
β Scribed by A. Duane Porter
- Publisher
- John Wiley and Sons
- Year
- 1966
- Tongue
- English
- Weight
- 125 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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.
We exhibit a deterministic algorithm for factoring polynomials in one variable over "nite "elds. It is e$cient only if a positive integer k is known for which I (p) is built up from small prime factors; here I denotes the kth cyclotomic polynomial, and p is the characteristic of the "eld. In the cas
We get an explicit formula for the number of solutions of a diagonal equation over finite fields, under a certain natural restriction on the exponents.
In this paper, we obtain a su$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