Electronic Theses and Dissertations

Date of Award

2019

Document Type

Thesis

Degree Name

M.S. in Mathematics

Department

Mathematics

First Advisor

Thái Lê

Second Advisor

Erwin Díaz

Third Advisor

Rizwanur Khan

Relational Format

dissertation/thesis

Abstract

The law of quadratic reciprocity is an important result in number theory. The purpose of this thesis is to present several proofs as well as applications of the law of quadratic reciprocity. I will present three proofs of the quadratic reciprocity. We begin with a proof that depends on Gauss's lemma and Eisenstein's lemma. We then describe another proof due to Eisentein using the $n$th roots of unity. Then we provide a modern proof published in 1991 by Rousseau. In the second part of the thesis, we present two applications of quadratic reciprocity. These include special cases of Dirichlet's theorem on primes in arithmetic progressions and Fermat's theorem on sums of two squares.

Included in

Mathematics Commons

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