The generalized fermat conjecture

Abstract. If a; b; c are non-zero integers, we considerer the following problem: for which values of n the line ax + by + cz = 0 may be tangent to the curve xn + yn = zn? We give a partial solution: if n = 5 or if n - 1 is a prime a number, then the answer is the line cannot be tangent to the curve....

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Autores:
García Máynez, Adalberto
Gary, Margarita
Pimienta Acosta, Adolfo
Tipo de recurso:
Fecha de publicación:
2019
Institución:
Universidad Simón Bolívar
Repositorio:
Repositorio Digital USB
Idioma:
eng
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oai:bonga.unisimon.edu.co:20.500.12442/2878
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http://hdl.handle.net/20.500.12442/2878
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spelling Licencia de Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2García Máynez, Adalberto95594f67-73c4-47b6-922b-b16df4006fdf-1Gary, Margarita855cc96f-25a5-4f30-8d5f-564849547f53-1Pimienta Acosta, Adolfoe342d5bd-4434-4e5e-ad0d-241c9099e23a-12019-04-05T16:47:20Z2019-04-05T16:47:20Z201901399918http://hdl.handle.net/20.500.12442/2878Abstract. If a; b; c are non-zero integers, we considerer the following problem: for which values of n the line ax + by + cz = 0 may be tangent to the curve xn + yn = zn? We give a partial solution: if n = 5 or if n - 1 is a prime a number, then the answer is the line cannot be tangent to the curve. This problem is strongly related to Fermat' s Last Theorem.engSpringerMathematica SlovacaVol. 69 No. 2 (2019)DOI: 10.1515/ms-2017-0225The generalized fermat conjecturearticlehttp://purl.org/coar/resource_type/c_6501B. Fine and G. Rosenberger. Classification of all generating pairs of two generator Fuchsian groups. London Math. Soc. Lecture Note Ser. 211, (1995) 205-232.D. J. H. Garling. A Course in Galois Theory. Cambridge University Press, 1986.S. Lang. Cyclotomic Fields I and II. Graduate Texts in Mathematics, 121, Springer-Verlag, New York, 1990.J. H. Silverman. Advanced Topics in the Arithmetic of Elliptic Curves. Graduate Texts in Mathematics, 151, Springer-Verlag, New York, 1994.L. Washington. Introduction to Cyclotomic Fields. Graduate Texts in Mathematics, Springer-Verlag, New York, 1996.A. Wiles. Modular elliptic curves and Fermat's Last Theorem. Ann. Math. 141 (1995), 443-551.ORIGINALPDF.pdfPDF.pdfPDFapplication/pdf271135https://bonga.unisimon.edu.co/bitstreams/f08a502e-cfeb-4c9f-9dcc-a1b5f483d93b/downloadd7656d8272957dd65b86830eda6cd08fMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-8368https://bonga.unisimon.edu.co/bitstreams/3ae94361-c4bd-4361-8ddf-5c4af0a4d8f6/download3fdc7b41651299350522650338f5754dMD52TEXTThe generalized fermat conjecture.pdf.txtThe generalized fermat conjecture.pdf.txtExtracted texttext/plain13721https://bonga.unisimon.edu.co/bitstreams/4038663b-96b5-452d-8f22-6e1a1405d3c0/downloadb570c9b6efe84c80cf9c518b85fd16d2MD53PDF.pdf.txtPDF.pdf.txtExtracted texttext/plain14136https://bonga.unisimon.edu.co/bitstreams/967e3d0f-09c2-4fbc-85fd-eefeaa927afd/downloada2ff7d9f1768890cdbe60d7802860357MD55THUMBNAILThe generalized fermat conjecture.pdf.jpgThe generalized fermat conjecture.pdf.jpgGenerated Thumbnailimage/jpeg1383https://bonga.unisimon.edu.co/bitstreams/40a7ed21-49af-4b64-922b-dd5149e1ce7e/download21f3a41495f850d52eaa1ff9e7ab23e1MD54PDF.pdf.jpgPDF.pdf.jpgGenerated Thumbnailimage/jpeg3511https://bonga.unisimon.edu.co/bitstreams/9f6d0347-a35c-486d-aceb-551a1faebf3c/downloadce2d2549cb2be63a67e65d31830158cdMD5620.500.12442/2878oai:bonga.unisimon.edu.co:20.500.12442/28782024-07-26 03:11:17.556open.accesshttps://bonga.unisimon.edu.coRepositorio Digital Universidad Simón Bolívarrepositorio.digital@unisimon.edu.coPGEgcmVsPSJsaWNlbnNlIiBocmVmPSJodHRwOi8vY3JlYXRpdmVjb21tb25zLm9yZy9saWNlbnNlcy9ieS1uYy80LjAvIj48aW1nIGFsdD0iTGljZW5jaWEgQ3JlYXRpdmUgQ29tbW9ucyIgc3R5bGU9ImJvcmRlci13aWR0aDowIiBzcmM9Imh0dHBzOi8vaS5jcmVhdGl2ZWNvbW1vbnMub3JnL2wvYnktbmMvNC4wLzg4eDMxLnBuZyIgLz48L2E+PGJyLz5Fc3RhIG9icmEgZXN0w6EgYmFqbyB1bmEgPGEgcmVsPSJsaWNlbnNlIiBocmVmPSJodHRwOi8vY3JlYXRpdmVjb21tb25zLm9yZy9saWNlbnNlcy9ieS1uYy80LjAvIj5MaWNlbmNpYSBDcmVhdGl2ZSBDb21tb25zIEF0cmlidWNpw7NuLU5vQ29tZXJjaWFsIDQuMCBJbnRlcm5hY2lvbmFsPC9hPi4=
dc.title.eng.fl_str_mv The generalized fermat conjecture
title The generalized fermat conjecture
spellingShingle The generalized fermat conjecture
title_short The generalized fermat conjecture
title_full The generalized fermat conjecture
title_fullStr The generalized fermat conjecture
title_full_unstemmed The generalized fermat conjecture
title_sort The generalized fermat conjecture
dc.creator.fl_str_mv García Máynez, Adalberto
Gary, Margarita
Pimienta Acosta, Adolfo
dc.contributor.author.none.fl_str_mv García Máynez, Adalberto
Gary, Margarita
Pimienta Acosta, Adolfo
description Abstract. If a; b; c are non-zero integers, we considerer the following problem: for which values of n the line ax + by + cz = 0 may be tangent to the curve xn + yn = zn? We give a partial solution: if n = 5 or if n - 1 is a prime a number, then the answer is the line cannot be tangent to the curve. This problem is strongly related to Fermat' s Last Theorem.
publishDate 2019
dc.date.accessioned.none.fl_str_mv 2019-04-05T16:47:20Z
dc.date.available.none.fl_str_mv 2019-04-05T16:47:20Z
dc.date.issued.none.fl_str_mv 2019
dc.type.eng.fl_str_mv article
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
dc.identifier.issn.none.fl_str_mv 01399918
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/20.500.12442/2878
identifier_str_mv 01399918
url http://hdl.handle.net/20.500.12442/2878
dc.language.iso.eng.fl_str_mv eng
language eng
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rights_invalid_str_mv Licencia de Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacional
http://purl.org/coar/access_right/c_abf2
dc.publisher.eng.fl_str_mv Springer
dc.source.eng.fl_str_mv Mathematica Slovaca
dc.source.spa.fl_str_mv Vol. 69 No. 2 (2019)
institution Universidad Simón Bolívar
dc.source.uri.spa.fl_str_mv DOI: 10.1515/ms-2017-0225
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