ON THE NUMBER OF SOLUTIONS TO CERTAIN DIAGONAL EQUATIONS OVER FINITE FIELDS
Ioulia N. Baoulina · International Journal of Number Theory · 2010
We consider a diagonal equation, which can be reduced to the form [Formula: see text] over a finite field of characteristic p > 2. In 1997, Sun obtained the explicit formula for the number of solutions to an equation of this type when n is even. In this paper, we find explicit formulas for the number of solutions when n is odd, k = 2rh, and there exists a positive integer ℓ such that pℓ ≡ 2m-1h + 1 ( mod 2mh), m = 3 or 4, r ≥ m, h = 1 or 3.