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On Certain Sum Involving Quadratic Residue

Author

Listed:
  • Kai An Sim

    (School of Mathematical Sciences, Sunway University, Petaling Jaya 47500, Malaysia
    These authors contributed equally to this work.)

  • Kok Bin Wong

    (Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia
    These authors contributed equally to this work.)

Abstract

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

Suggested Citation

  • Kai An Sim & Kok Bin Wong, 2022. "On Certain Sum Involving Quadratic Residue," Mathematics, MDPI, vol. 10(12), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:1981-:d:834295
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    Keywords

    sumset; quadratic residue;

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