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World Scientific Publishing, International Journal of Number Theory, 08(16), p. 1833-1858, 2020

DOI: 10.1142/s1793042120500955

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Quadratic residues and quartic residues modulo primes

Journal article published in 2020 by Zhi-Wei Sun ORCID
This paper was not found in any repository, but could be made available legally by the author.
This paper was not found in any repository, but could be made available legally by the author.

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Abstract

In this paper, we study some products related to quadratic residues and quartic residues modulo primes. Let [Formula: see text] be an odd prime and let [Formula: see text] be any integer. We determine completely the product [Formula: see text] modulo [Formula: see text]; for example, if [Formula: see text] then [Formula: see text] where [Formula: see text] denotes the Legendre symbol. We also determine [Formula: see text] modulo [Formula: see text].