科研之友
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摘要
Let n > 1 be an integer, and let F-p 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-p 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-p. We also prove the nonexistence of qualified 24-th power residue difference sets in F-p. 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.
- 出版日期2017-7
