{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/57168"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/57168","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"Quadratic Forms Representing All Integers Coprime to 3","abstract":"Drawing up on the methods developed by Bhargava to prove \"The Fifteen Theorem\" and expanded by Rouse when handling integer-valued quadratic forms representing odd integers, we show that an integer-valued quadratic form representing all positive integers coprime to 3 up to 290 must represent all positive integers coprime to 3. We further this result by enumerating a list of 31 critical numbers such that representing all numbers on the list guarantees an integer-valued quadratic form represents all positive integers coprime to 3. Finally, we show that no numbers can be removed from this list.","abstract_html":"Drawing up on the methods developed by Bhargava to prove "The Fifteen Theorem" and expanded by Rouse when handling integer-valued quadratic forms representing odd integers, we show that an integer-valued quadratic form representing all positive integers coprime to 3 up to 290 must represent all positive integers coprime to 3. We further this result by enumerating a list of 31 critical numbers such that representing all numbers on the list guarantees an integer-valued quadratic form represents all positive integers coprime to 3. Finally, we show that no numbers can be removed from this list.","abstract_has_math":false,"creators":["DeBenedetto, Justin Donald"],"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":2015,"date_issued":"2015","date_published":"2015","updated_at":"2026-07-27T22:01:52Z","subjects":["Local Density"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10339/57168","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["DeBenedetto, Justin Donald"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-06-23T08:35:57Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-06-23T08:35:57Z"]},{"key":"dc:date.issued","label":"Date","values":["2015"]},{"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":["Local Density"]}]},{"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/10339/57168"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Drawing up on the methods developed by Bhargava to prove \"The Fifteen Theorem\" and expanded by Rouse when handling integer-valued quadratic forms representing odd integers, we show that an integer-valued quadratic form representing all positive integers coprime to 3 up to 290 must represent all positive integers coprime to 3. We further this result by enumerating a list of 31 critical numbers such that representing all numbers on the list guarantees an integer-valued quadratic form represents all positive integers coprime to 3. Finally, we show that no numbers can be removed from this list."]},{"key":"dc:title","label":"Title","values":["Quadratic Forms Representing All Integers Coprime to 3"]}]}],"canonical_facts":{"dc:creator":["DeBenedetto, Justin Donald"],"dc:date.accessioned":["2015-06-23T08:35:57Z"],"dc:date.available":["2015-06-23T08:35:57Z"],"dc:date.issued":["2015"],"dc:description.abstract":["Drawing up on the methods developed by Bhargava to prove \"The Fifteen Theorem\" and expanded by Rouse when handling integer-valued quadratic forms representing odd integers, we show that an integer-valued quadratic form representing all positive integers coprime to 3 up to 290 must represent all positive integers coprime to 3. We further this result by enumerating a list of 31 critical numbers such that representing all numbers on the list guarantees an integer-valued quadratic form represents all positive integers coprime to 3. Finally, we show that no numbers can be removed from this list."],"dc:identifier.uri":["http://hdl.handle.net/10339/57168"],"dc:language.iso":["en"],"dc:publisher":["Wake Forest University"],"dc:subject":["Local Density"],"dc:title":["Quadratic Forms Representing All Integers Coprime to 3"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:01:52Z"}