Nonexistence of twenty-fourth power residue addition sets
Number Theory
2016-11-24 v1
Abstract
Let n > 1 be an integer, and let F denote a field of p elements for a prime p = 1 (mod n). By 2015, the question of existence or nonexistence of n-th power residue difference sets in F 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 F. We also prove the nonexistence of qualified 24-th power residue difference sets in F. 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.
Keywords
Cite
@article{arxiv.1611.07646,
title = {Nonexistence of twenty-fourth power residue addition sets},
author = {Ron Evans and Mark Van Veen},
journal= {arXiv preprint arXiv:1611.07646},
year = {2016}
}
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10 pages