@article{Hu2022, 
author = {Shuangnian Hu and Rongquan Feng},
title = {On the number of solutions of two-variable diagonal sextic equations over finite fields},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {6},
pages = {10554-10563},
keywords = {finite fields, rational points, diagonal equations, Jacobi sums},
url = {https://www.sciopen.com/article/10.3934/math.2022588},
doi = {10.3934/math.2022588},
abstract = {Let    p be a prime,    k a positive integer,    q  =      p    k  , and              F        q   be the finite field with    q elements. In this paper, by using the Jacobi sums, we give an explicit formula for the number of solutions of the two-variable diagonal sextic equations        x    1    6    +      x    2    6    =  c over              F        q  , with    c  ∈            F        q    ∗   and    p  ≡  1  (            m      o      d          6  ). Furthermore, by using the reduction formula for Jacobi sums, the number of solutions of the diagonal sextic equations        x    1    6    +      x    2    6    +  ⋯  +      x    n    6    =  c of    n  ≥  3 variables with    c  ∈            F        q    ∗   and    p  ≡  1  (            m      o      d          6  ), can also be deduced.}
}