International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 19, Pages 1175-1183
doi:10.1155/S0161171203206256
On the special solutions of an equation in a finite field
1Department of Mathematics, Weinan Teacher's College, Weinan, Shaanxi, China
2Research Center for Basic Science, Xi'an Jiaotong University, Xi'an, Shaanxi, China
Received 10 June 2002
Copyright © 2003 Li Hailong and Zhang Wenpeng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The main purpose of this paper is to prove the following
conclusion: let p be a prime large enough and let k be a fixed positive integer with 2k|p−1. Then for any finite field Fp and any element 0≠c∈Fp, there exist three generators x, y, and z∈Fp such that xkyk+ykzk+xkzk=c.