{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T01:16:23Z","timestamp":1782782183081,"version":"3.54.5"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,7,2]]},"abstract":"<jats:p xml:lang=\"en\">We formalize a complete proof of the regular case of Fermat's Last Theorem in the Lean4 theorem prover. Our formalization includes a proof of Kummer's lemma, that is the main obstruction to Fermat's Last Theorem for regular primes. Rather than following the modern proof of Kummer's lemma via class field theory, we prove it by using Hilbert's Theorems 90-94 in a way that is more amenable to formalization.<\/jats:p>","DOI":"10.46298\/afm.14586","type":"journal-article","created":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T14:55:13Z","timestamp":1752591313000},"source":"Crossref","is-referenced-by-count":1,"title":["A complete formalization of Fermat's Last Theorem for regular primes in Lean"],"prefix":"10.46298","volume":"Volume 1","author":[{"given":"Alex","family":"Best","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05f82e368","id-type":"ROR","asserted-by":"publisher"}],"name":"Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche","acronym":["UPCit\u00e9"]},{"id":[{"id":"https:\/\/ror.org\/05f82e368","id-type":"ROR","asserted-by":"publisher"}],"name":"Universit\u00e9 Paris Cit\u00e9","acronym":["UPCit\u00e9"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7546-9028","authenticated-orcid":false,"given":"Christopher","family":"Birkbeck","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/026k5mg93","id-type":"ROR","asserted-by":"publisher"}],"name":"University of East Anglia [Norwich]","acronym":["UEA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0507-627X","authenticated-orcid":false,"given":"Riccardo","family":"Brasca","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5741-674X","authenticated-orcid":false,"given":"Eric","family":"Rodriguez Boidi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruben van De","family":"Velde","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrew","family":"Yang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/041kmwe10","id-type":"ROR","asserted-by":"publisher"}],"name":"Imperial College London"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"25203","published-online":{"date-parts":[[2025,7,15]]},"container-title":["Annals of Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/hal.science\/hal-04718128v4\/document","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/hal.science\/hal-04718128v4\/document","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T14:55:16Z","timestamp":1752591316000},"score":1,"resource":{"primary":{"URL":"https:\/\/afm.episciences.org\/14586"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,15]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/afm.14586","relation":{"has-preprint":[{"id-type":"uri","id":"https:\/\/hal.science\/hal-04718128v3","asserted-by":"subject"},{"id-type":"uri","id":"https:\/\/hal.science\/hal-04718128v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"uri","id":"https:\/\/hal.science\/hal-04718128v4","asserted-by":"subject"}]},"subject":[],"published":{"date-parts":[[2025,7,15]]},"article-number":"14586"}}