On a conjecture on exponential Diophantine equations
Mihai Cipu, Maurice Mignotte (2009)
Acta Arithmetica
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Mihai Cipu, Maurice Mignotte (2009)
Acta Arithmetica
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Maohua Le (2001)
Acta Arithmetica
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N. Saradha (2012)
Acta Arithmetica
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Zhenfu Cao, Xiaolei Dong (2003)
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.
Andrej Dujella, Alan Filipin, Clemens Fuchs (2007)
Acta Arithmetica
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Acu, Dumitru (2001)
General Mathematics
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Shanta Laishram, T. N. Shorey (2012)
Acta Arithmetica
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Leo J. Alex, Lorraine L. Foster (1995)
Forum mathematicum
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Mario Huicochea (2010)
Acta Arithmetica
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E. Herrmann, I. Járási, A. Pethő (2004)
Acta Arithmetica
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Yann Bugeaud, Michael Drmota, Bernard de Mathan (2007)
Acta Arithmetica
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Yu. F. Bilu, M. Kulkarni, B. Sury (2004)
Acta Arithmetica
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Susil Kumar Jena (2014)
Colloquium Mathematicae
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We prove that for each n ∈ ℕ₊ the Diophantine equation A² ± nB⁴ + C⁴ = D⁸ has infinitely many primitive integer solutions, i.e. solutions satisfying gcd(A,B,C,D) = 1.
Clemens Heuberger (2001)
Acta Arithmetica
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Jingcheng Tong (1991)
Monatshefte für Mathematik
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András Biró (2003)
Acta Arithmetica
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Csaba Rakaczki (2003)
Acta Arithmetica
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A. D. Pollington, R. C. Vaughan (1989)
Journal de théorie des nombres de Bordeaux
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We show that the Duffin and Schaeffer conjecture holds in all dimensions greater than one.
J. H. E. Cohn (2003)
Acta Arithmetica
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