On the special solutions of an equation in a finite field
LI Hai-long, Wenpeng Zhang · International Journal of Mathematics and Mathematical Sciences · 2003
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.