On the diophantine equation f (x, y) = 0.
H. Kleiman (1976)
Journal für die reine und angewandte Mathematik
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H. Kleiman (1976)
Journal für die reine und angewandte Mathematik
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Ernst, Bruno (1996)
General Mathematics
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Alan Filipin (2009)
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.
Yang Hai, P. G. Walsh (2010)
Acta Arithmetica
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Shin-ichi Katayama, Claude Levesque (2003)
Acta Arithmetica
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W. J. Ellison (1970-1971)
Séminaire de théorie des nombres de Bordeaux
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J. H. E. Cohn (2003)
Acta Arithmetica
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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:
S. Akhtari, A. Togbé, P. G. Walsh (2009)
Acta Arithmetica
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Jianhua Chen (2001)
Acta Arithmetica
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Xiaolei Dong, W. C. Shiu, C. I. Chu, Zhenfu Cao (2007)
Acta Arithmetica
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Pingzhi Yuan, Jiagui Luo (2010)
Acta Arithmetica
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Umberto Zannier (2003)
Acta Arithmetica
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M. Filaseta, F. Luca, P. Stănică, R. G. Underwood (2007)
Acta Arithmetica
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Muriefah, Fadwa S.Abu, Bugeaud, Yann (2006)
Revista Colombiana de Matemáticas
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Pingzhi Yuan (2004)
Acta Arithmetica
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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.
E. Herrmann, I. Járási, A. Pethő (2004)
Acta Arithmetica
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