Article ID Journal Published Year Pages File Type
4583216 Finite Fields and Their Applications 2007 5 Pages PDF
Abstract

In 1988 Garcia and Voloch proved the upper bound 4n4/3(p−1)2/3 for the number of solutions over a prime finite field Fp of the Fermat equation xn+yn=a, where and n⩾2 is a divisor of p−1 such that . This is better than Weil's bound in the stated range. By refining Garcia and Voloch's proof we show that the constant 4 in their bound can be replaced by 3⋅2−2/3.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory