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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Consecutive numbers with the same Legendre symbol


Author: Zhi-Hong Sun
Journal: Proc. Amer. Math. Soc. 130 (2002), 2503-2507
MSC (2000): Primary 11A15; Secondary 11A07
Published electronically: April 17, 2002
MathSciNet review: 1900855
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Abstract: Let $p$ be an odd prime, and $R_{p}$ be a complete set of residues $(\text{\rm mod} p)$. The goal of the paper is to determine all the values of $n (n\in R_{p})$ such that $\big (\frac{n}{p}\big ) = \big (\frac{n+1}{p}\big )$ or $\big (\frac{n-1}{p}\big )= \big (\frac{n}{p}\big ) =\big (\frac{n+1}{p}\big )$, where $\big (\frac{\cdot }{p}\big ) $ is the Legendre symbol.


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Additional Information

Zhi-Hong Sun
Affiliation: Department of Mathematics, Huaiyin Teachers College, Huaian, Jiangsu 223001, People’s Republic of China
Email: hyzhsun@public.hy.js.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06600-5
PII: S 0002-9939(02)06600-5
Keywords: Prime, Legendre symbol
Received by editor(s): February 27, 2001
Published electronically: April 17, 2002
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2002 American Mathematical Society