{"id":{"repo_id":"mississippi","oai_identifier":"oai:egrove.olemiss.edu:etd-2539"},"canonical_url":"https://search.dev.ndltd.org/etd/mississippi/oai:egrove.olemiss.edu:etd-2539","repository":{"repo_id":"mississippi","name":"University of Mississippi","base_url":"https://egrove.olemiss.edu/do/oai/"},"display":{"title":"Quadratic Reciprocity: Proofs and Applications","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.","abstract_html":"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.","abstract_has_math":true,"creators":["Almuteri, Awatef Noweafa"],"institution":null,"degree_name":"M.S. in Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Thai Hoang Le","Erwin Mina Diaz","Rizwanur Khan"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-01-01T08:00:00Z","date_published":"2019-01-01T08:00:00Z","updated_at":"2026-07-24T03:07:00Z","subjects":["3D Printing","Additive construction","GnP","MPC paste","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://egrove.olemiss.edu/etd/1540","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Thai Hoang Le","Erwin Mina Diaz","Rizwanur Khan"]},{"key":"dc:creator","label":"Author","values":["Almuteri, Awatef Noweafa"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2020-01-23T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S. in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["3D Printing","Additive construction","GnP","MPC paste","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://egrove.olemiss.edu/etd/1540"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Quadratic Reciprocity: Proofs and Applications"]}]}],"canonical_facts":{"dc:contributor":["Thai Hoang Le","Erwin Mina Diaz","Rizwanur Khan"],"dc:creator":["Almuteri, Awatef Noweafa"],"dc:date.available":["2020-01-23T08:00:00Z"],"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."],"dc:identifier":["https://egrove.olemiss.edu/etd/1540"],"dc:subject":["3D Printing","Additive construction","GnP","MPC paste","Mathematics"],"dc:title":["Quadratic Reciprocity: Proofs and Applications"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S. in Mathematics"]},"updated_at":"2026-07-24T03:07:00Z"}