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