On certain sum involving quadratic residue

Document Type

Article

Publication Date

6-1-2022

Abstract

Let p be a prime and F-p be the set of integers modulo p. Let chi(p) be a function defined on F-p such that chi(p)(0) = 0 and for a is an element of F-p\textbackslash{0}, set chi(p)(a) = 1 if a is a quadratic residue modulo p and chi(p)(a)= -1 if a is a quadratic non-residue modulo p. Note that chi(p)(a)=(a/p) is indeed the Legendre symbol. The image of chi(p) in the set of real numbers. In this paper, we consider the following sum Sigma(x is an element of Fp)chi(p)((x-a(1))(x-a(2))...(x-a(t))) where a(1),a(2), ...,a(t) are distinct elements in F-p.

Keywords

Sumset, Quadratic residue

Divisions

MathematicalSciences

Funders

Sunway University, Malaysia

Publication Title

Mathematics

Volume

10

Issue

12

Publisher

MDPI

Publisher Location

ST ALBAN-ANLAGE 66, CH-4052 BASEL, SWITZERLAND

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