{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/37265"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/37265","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"Solutions of the Cubic Fermat Equation in Quadratic Fields","abstract":"We will examine when there are nontrivial solutions to the equation $x^3 + y^3 = z^3$ in $\\mathbb{Q}(\\sqrt{d})$ for a squarefree integer $d$. In this variation of Fermat's Last Theorem, it is possible for nontrivial solutions to exist in $\\mathbb{Q}(\\sqrt{d})$ for some choices of $d$, but not for all. Our argument assumes the Birch and Swinnerton-Dyer conjecture and follows a similar argument as Tunnell's solution to the congruent number problem.","abstract_html":"We will examine when there are nontrivial solutions to the equation <span class=\"etd-inline-math\">x<sup>3</sup> + y<sup>3</sup> = z<sup>3</sup></span> in $\\mathbb{Q}(\\sqrt{d})$ for a squarefree integer $d$. In this variation of Fermat&#x27;s Last Theorem, it is possible for nontrivial solutions to exist in $\\mathbb{Q}(\\sqrt{d})$ for some choices of $d$, but not for all. Our argument assumes the Birch and Swinnerton-Dyer conjecture and follows a similar argument as Tunnell&#x27;s solution to the congruent number problem.","abstract_has_math":true,"creators":["Jones, Marvin"],"institution":"Wake Forest University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012","date_published":"2012","updated_at":"2026-07-27T22:01:27Z","subjects":["elliptic curves"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10339/37265","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Jones, Marvin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2012-06-12T08:35:51Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2012-06-12T08:35:51Z"]},{"key":"dc:date.issued","label":"Date","values":["2012"]},{"key":"dc:publisher","label":"Institution","values":["Wake Forest University"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["elliptic curves"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10339/37265"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We will examine when there are nontrivial solutions to the equation $x^3 + y^3 = z^3$ in $\\mathbb{Q}(\\sqrt{d})$ for a squarefree integer $d$. In this variation of Fermat's Last Theorem, it is possible for nontrivial solutions to exist in $\\mathbb{Q}(\\sqrt{d})$ for some choices of $d$, but not for all. Our argument assumes the Birch and Swinnerton-Dyer conjecture and follows a similar argument as Tunnell's solution to the congruent number problem."]},{"key":"dc:title","label":"Title","values":["Solutions of the Cubic Fermat Equation in Quadratic Fields"]}]}],"canonical_facts":{"dc:creator":["Jones, Marvin"],"dc:date.accessioned":["2012-06-12T08:35:51Z"],"dc:date.available":["2012-06-12T08:35:51Z"],"dc:date.issued":["2012"],"dc:description.abstract":["We will examine when there are nontrivial solutions to the equation $x^3 + y^3 = z^3$ in $\\mathbb{Q}(\\sqrt{d})$ for a squarefree integer $d$. In this variation of Fermat's Last Theorem, it is possible for nontrivial solutions to exist in $\\mathbb{Q}(\\sqrt{d})$ for some choices of $d$, but not for all. Our argument assumes the Birch and Swinnerton-Dyer conjecture and follows a similar argument as Tunnell's solution to the congruent number problem."],"dc:identifier.uri":["http://hdl.handle.net/10339/37265"],"dc:language.iso":["en"],"dc:publisher":["Wake Forest University"],"dc:subject":["elliptic curves"],"dc:title":["Solutions of the Cubic Fermat Equation in Quadratic Fields"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:01:27Z"}