Zeros of Diagonal Equations over Finite Fields

Daqing Wan
1988 Proceedings of the American Mathematical Society  
Let N be the number of solutions (xi, ■ ■ ■ ,xn) of the equation (1) CiZj1 + C2I22 "I-+ CnXnn = C over the finite field Fq, where d,|(g -1), c¡ e F* (»si,... ,n), and c S Fq. If 11 1 dl ¿2 dn for some positive integer b, we prove that qb\N. This result is an improvement of the theorem that p\N obtained by B. Morlaye [7] and also by J. R. Joly [3].
doi:10.2307/2047083 fatcat:reodroatcvaoxlgwhw5zfcsclu