On the special solutions of an equation in a finite field (Q1811897)

Summary: 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 \(F_p\) and any element \(0\neq c\in F_{p}\), there exist three generators \(x\), \(y\), and \(z\in F_{p}\) such that \(x^{k}y^{k}+y^{k}z^{k}+x^{k}z^{k}=c\).