Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771653 | Finite Fields and Their Applications | 2017 | 8 Pages |
Abstract
Let n>1 be an integer, and let Fp denote a field of p elements for a prime pâ¡1(modn). By 2015, the question of existence or nonexistence of n-th power residue difference sets in Fp had been settled for all n<24. We settle the case n=24 by proving the nonexistence of 24-th power residue difference sets in Fp. We also prove the nonexistence of qualified 24-th power residue difference sets in Fp. The proofs make use of a Mathematica program which computes formulas for the cyclotomic numbers of order 24 in terms of parameters occurring in quadratic partitions of p.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ron Evans, Mark Van Veen,