On the Diophantine system \(a^2+ b^2 = c^3\) and \(a^x + b^y = c^z\) for \(b\) is an odd prime

DOI10.1007/s10114-007-6140-xzbMath1218.11037OpenAlexW2170973039MaRDI QIDQ943531

Maohua Le

Publication date: 9 September 2008

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-007-6140-x

zbMATH Keywords

exponential Diophantine equationpositive integer solutiongeneralized Fermat conjecture

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61)

Cites Work

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• The diophantine equation \(a^ x+b^ y=c^ z\)
• A note on the diophantine equation \((m^3-3m)^x+(3m^2-1)^y=(m^2+1)^z\)
• Zur Approximation algebraischer Zahlen. I: Über den grössten Primteiler binärer Formen
• Some exponential diophantine equations. I: The equation \(D_1x^2 - D_2y^2 = \lambda k^z\)
• Existence of primitive divisors of Lucas and Lehmer numbers
• A note on the Diophantine equation $a^x + b^y = c^z$
• Primitive Divisors of Lucas and Lehmer Sequences
• On the Equations z^m = F (x, y ) and Ax^p + By^q = Cz^r

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