› Electronic Theses and Dissertations

# Solutions of the Cubic Fermat Equation in Quadratic Fields

## Electronic Theses and Dissertations

### Item Details

title
Solutions of the Cubic Fermat Equation in Quadratic Fields
author
Jones, Marvin
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.
subject
elliptic curves
fermat's last theorem
modular forms
contributor
Rouse, Jeremy A (committee chair)
Howard, Fredric T (committee member)
Berenhaut, Kenneth S (committee member)
date
2012-06-12T08:35:51Z (accessioned)
2012-06-12T08:35:51Z (available)
2012 (issued)
degree
Mathematics (discipline)
identifier
http://hdl.handle.net/10339/37265 (uri)
language
en (iso)
publisher
Wake Forest University
type
Thesis
{"ft_lang_label":"__label__en","ft_lang_prob":0.6922041,"math_prob":0.84530264,"size":1222,"snap":"2023-40-2023-50","text_gpt3_token_len":347,"char_repetition_ratio":0.09031199,"word_repetition_ratio":0.05464481,"special_character_ratio":0.27741408,"punctuation_ratio":0.08290155,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9636817,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-03T13:45:41Z\",\"WARC-Record-ID\":\"<urn:uuid:aad00d36-fc29-44b1-971d-2ba40d41e746>\",\"Content-Length\":\"13201\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5c5a6c72-05c0-4931-b3d6-8258ae235ce4>\",\"WARC-Concurrent-To\":\"<urn:uuid:e4103287-d4d0-4ceb-b1bc-75fe10b07b57>\",\"WARC-IP-Address\":\"54.235.104.220\",\"WARC-Target-URI\":\"https://wakespace.lib.wfu.edu/handle/10339/37265\",\"WARC-Payload-Digest\":\"sha1:YVOCP3HCW7BL7PVJGTZVK37PE3S3ILX5\",\"WARC-Block-Digest\":\"sha1:BX3FJXFQYRBQA3SC5GGPBKRBT2Y5BKJK\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100508.23_warc_CC-MAIN-20231203125921-20231203155921-00363.warc.gz\"}"}