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On the exponential Diophantine equation \(a^x+b^y=c^z\)

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Publication:1607592
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DOI10.3792/pjaa.77.151zbMath1009.11026OpenAlexW1972942094MaRDI QIDQ1607592

Nobuhiro Terai

Publication date: 1 May 2003

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.77.151


zbMATH Keywords

congruence conditions


Mathematics Subject Classification ID

Exponential Diophantine equations (11D61)


Related Items (1)

A note on the exponential Diophantine equation \(a^x+b^y=c^z\)



Cites Work

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  • On the equations \(p^x - b^y = c\) and \(a^x + b^y = c^z\)
  • The Diophantine equation \(x^ 2\pm \ell y^ 2=z^{\ell}\) connected with Fermat's Last Theorem
  • Linear forms in two logarithms and interpolation determinants
  • On the Diophantine equation \(Cx^ 2 +D = y^ n\)
  • Diophantine equations of the form x2 + D = yn.
  • Diophantine eaquations of the form ax2 + Db2 = yp.
  • A corollary to a theorem of Laurent-Mignotte-Nesterenko
  • Applications of a lower bound for linear forms in two logarithms to exponential Diophantine equations
  • A note on the Diophantine equation $a^x + b^y = c^z$


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