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Proceedings of the American Mathematical Society

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Maximal residue difference sets modulo $ p$


Authors: Duncan A. Buell and Kenneth S. Williams
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
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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 [Enhancements On Off] (What's this?)

  • [1] D. A. Burgess, The distribution of quadratic residues and non-residues, Mathematika 4 (1957), 106-112. MR 0093504 (20:28)
  • [2] -, On character sums and primitive roots, Proc. London Math. Soc. (3) 12 (1962), 179-192. MR 0132732 (24:A2569)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0498345-0
Article copyright: © Copyright 1978 American Mathematical Society

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