The Diophantine equation : a brief overview.
Muriefah, Fadwa S.Abu, Bugeaud, Yann (2006)
Revista Colombiana de Matemáticas
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Muriefah, Fadwa S.Abu, Bugeaud, Yann (2006)
Revista Colombiana de Matemáticas
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Enrico Bombieri (2000)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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This lecture is a survey of recent results in the theory of diophantine equations, especially for dimension 1. The unit equation and its generalizations are examined in detail, as well as Baker's theory and the consequences of the abc-conjecture.
Andrej Dujella, Alan Filipin, Clemens Fuchs (2007)
Acta Arithmetica
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Alan Filipin (2009)
Acta Arithmetica
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Franušić, Zrinka (2010)
Journal of Integer Sequences [electronic only]
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Samir Siksek (2009)
Journal de Théorie des Nombres de Bordeaux
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These are expository notes that accompany my talk at the 25th Journées Arithmétiques, July 2–6, 2007, Edinburgh, Scotland. I aim to shed light on the following two questions:
W. J. Ellison (1970-1971)
Séminaire de théorie des nombres de Bordeaux
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Umberto Zannier (2003)
Acta Arithmetica
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Ernst, Bruno (1996)
General Mathematics
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Yang Hai, P. G. Walsh (2010)
Acta Arithmetica
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S. Akhtari, A. Togbé, P. G. Walsh (2009)
Acta Arithmetica
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H. Kleiman (1976)
Journal für die reine und angewandte Mathematik
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Pingzhi Yuan, Jiagui Luo (2010)
Acta Arithmetica
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Utz, W.R. (1982)
International Journal of Mathematics and Mathematical Sciences
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Shin-ichi Katayama, Claude Levesque (2003)
Acta Arithmetica
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Susil Kumar Jena (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
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The Diophantine equation A² + nB⁴ = C³ has infinitely many integral solutions A, B, C for any fixed integer n. The case n = 0 is trivial. By using a new polynomial identity we generate these solutions, and then give conditions when the solutions are pairwise co-prime.