On the diophantine equation \(la^x + mb^y = nc^z\)

  • Sivanarayanapandian Subburam


In this paper, we give an upper bound for the solutions x, y, z of the equation in the title, of magnitude \(\left( \log \max \{a, b, c\}\right) ^{2 + \epsilon }\). This yields an improvement of earlier results of Hu and Le, where the bound is cubic in \(\log \max \{a, b, c\}\).


Exponential diophantine equation 

Mathematics Subject Classification

11D41 11D45 


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Copyright information

© SpringerNature 2018

Authors and Affiliations

  1. 1.AruppukottaiIndia

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