Consecutive numbers with the same Legendre symbol
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Abstract:
Let $p$ be an odd prime, and $R_{p}$ be a complete set of residues $(\operatorname {mod} p)$. 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.References
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Additional Information
- Zhi-Hong Sun
- Affiliation: Department of Mathematics, Huaiyin Teachers College, Huaian, Jiangsu 223001, People’s Republic of China
- MR Author ID: 318137
- Email: hyzhsun@public.hy.js.cn
- Received by editor(s): February 27, 2001
- Published electronically: April 17, 2002
- Communicated by: David E. Rohrlich
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2503-2507
- MSC (2000): Primary 11A15; Secondary 11A07
- DOI: https://doi.org/10.1090/S0002-9939-02-06600-5
- MathSciNet review: 1900855