Maximal residue difference sets modulo $p$
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- by Duncan A. Buell and Kenneth S. Williams PDF
- Proc. Amer. Math. Soc. 69 (1978), 205-209 Request permission
Abstract:
Let $p \equiv 1 \pmod 4$ be a prime. A residue difference set modulo p is a set $S = \{ {a_i}\}$ of integers ${a_i}$ such that $(\frac {{{a_i}}}{p}) = + 1$ and $(\frac {{{a_i} - {a_j}}}{p}) = + 1$ for all i and j with $i \ne j$, where $(\frac {n}{p})$ is the Legendre symbol modulo p. Let ${m_p}$ be the cardinality of a maximal such set S. The authors estimate the size of ${m_p}$.References
- D. A. Burgess, The distribution of quadratic residues and non-residues, Mathematika 4 (1957), 106–112. MR 93504, DOI 10.1112/S0025579300001157
- D. A. Burgess, On character sums and primitive roots, Proc. London Math. Soc. (3) 12 (1962), 179–192. MR 132732, DOI 10.1112/plms/s3-12.1.179
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 69 (1978), 205-209
- MSC: Primary 10A10; Secondary 05B10
- DOI: https://doi.org/10.1090/S0002-9939-1978-0498345-0
- MathSciNet review: 0498345