{"pk":59052,"title":"On the Applications of Cyclotomic Fields in Introductory Number Theory","subtitle":null,"abstract":"In this essay, we study and comment on two number theoretical applications on prime cyclotomic fields (cyclotomic fields obtained by adjoining a primitive p-th root of unity to Q, where p is an odd prime). We begin by giving a simplified proof of Kummer's case of Fermat's Last Theorem obtained by linking different versions of the proof in different textbooks. We finally modernize Dirichlet's solution to Pell's Equation.","language":"en","license":null,"keywords":[{"word":"Number Theory"},{"word":"Cyclotomic Fields"},{"word":"Pell's Equation"},{"word":"Dirichlet"},{"word":"Kummer"},{"word":"Fermat's Last Theorem"},{"word":"Primary Units"},{"word":"Real Units"},{"word":"mathematics"}],"section":"Research","is_remote":true,"remote_url":"https://escholarship.org/uc/item/49c0561x","frozenauthors":[{"first_name":"Kabalan","middle_name":"","last_name":"Gaspard","name_suffix":"","institution":"Mathematical Institute, Oxford University","department":""}],"date_submitted":"2013-03-05T03:50:05Z","date_accepted":"2013-03-05T03:50:05Z","date_published":"2013-03-04T08:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/our_bsj/article/59052/galley/45089/download/"}]}