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
Hailong Li1
and Wenpeng Zhang2
1Department of Mathematics, Weinan Teacher's College, Weinan, Shaanxi, China
2Research Center for Basic Science, Xi'an Jiaotong University, Xi'an, Shaanxi, China
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.