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Four Interesting Applications of Quadratic Reciprocity

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Quadratic Residues and Non-Residues

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2171))

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Abstract

Gauss called the Law of Quadratic Reciprocity the golden theorem of number theory because, when it is in hand, the study of quadratic residues and non-residues can be pursued to a significantly deeper level. We have already seen some examples of how useful the LQR can be in answering questions about specific residues or non-residues. In this chapter, we will study four applications of the LQR which illustrate how it can be used to shed further light on interesting properties of residues and non-residues.

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  1. Department of Mathematics and Statistics, Oakland University, Rochester, Michigan, USA

    Steve Wright

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Wright, S. (2016). Four Interesting Applications of Quadratic Reciprocity . In: Quadratic Residues and Non-Residues. Lecture Notes in Mathematics, vol 2171. Springer, Cham. https://doi.org/10.1007/978-3-319-45955-4_4

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