On certain sum involving quadratic residue
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(...
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| Main Authors: | , |
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| Format: | Article |
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MDPI
2022
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| Subjects: | |
| Online Access: | http://eprints.um.edu.my/41968/ |
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| Summary: | 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. |
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