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Consecutive numbers with the same Legendre symbol

Authors:	Zhi-Hong Sun

Affiliation:	Department of Mathematics, Huaiyin Teachers College, Huaian, Jiangsu 223001, People's Republic of China

Abstract:	Let be an odd prime, and $R_{p}$ be a complete set of residues . The goal of the paper is to determine all the values of $n (nin R_{p})$ 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.

Keywords:	Prime Legendre symbol

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