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University of Mississippi

Quadratic Reciprocity: Proofs and Applications

Abstract

dc:description.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.

Degree

thesis:*
Name thesis:degree_name
M.S. in Mathematics
Level thesis:degree_level
Thesis
Discipline thesis:degree_discipline
Mathematics
Year dc:date.available
2019

Author and committee

dc:creator, dc:contributor.*
Author dc:creator
  • Almuteri, Awatef Noweafa
Contributors dc:contributor
  • Thai Hoang Le
  • Erwin Mina Diaz
  • Rizwanur Khan

Subjects

dc:subject × 5

Identifiers

dc:identifier.*
Repository record dc:identifier
https://egrove.olemiss.edu/etd/1540
OAI identifier oai:identifier
oai:egrove.olemiss.edu:etd-2539

Chain of custody

source
Harvested from
University of Mississippi
Base URL
egrove.olemiss.edu/do/oai/
Last updated
2026-07-24
Source record
OAI-PMH GetRecord
citation

Almuteri, Awatef Noweafa. Quadratic Reciprocity: Proofs and Applications. Thesis thesis, 2019. https://egrove.olemiss.edu/etd/1540