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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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}$.


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