Abstract
Let p be an odd prime. In this article, we investigate the number of ways in which a quadratic residue and a non-residue modulo p can be expressed as sum of two quadratic residues sum of two quadratic non-residues, and sum of a quadratic residue and non-residue in an elementary way using Gauss sums.
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References
Apostol, T.M.: Introduction to Analytic Number Theory. Narosa Publishing House, Eighth Reprint, Springer International Student Edition (1998)
Gauss, C. F.: Disquisitiones Arithmeticae. Translated into English by Arthur A. Clarke. S.J. Yale University Press, New Haven, Conn.-London (1966)
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The authors would like to thank the anonymous referee for the valuable suggestions which really improved the quality of this article.
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M.V., Y., M.R., M. Partition of quadratic residues and non-residues in \(\mathbb {Z}_p^*\) for an odd prime p. Arch. Math. 122, 265–271 (2024). https://doi.org/10.1007/s00013-023-01942-2
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DOI: https://doi.org/10.1007/s00013-023-01942-2