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

Research
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Abstract

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 \(\log \max \{a, b, c\}\).

Keyword

Exponential diophantine equation 

Mathematics Subject Classification

11D41 11D45 

References

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    Hu, Y., Le, M.: A note on ternary purely exponential diophantine equations. Acta Arith. 171, 173–182 (2015)MathSciNetCrossRefMATHGoogle Scholar
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    Hu, Y., Le, M.: An upper bound for the number of solutions of ternary purely exponential diophantine equations. J. Number Theory 183, 62–73 (2018)MathSciNetCrossRefMATHGoogle Scholar
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    Shorey, T.N., Tijdeman, R.: Exponential Diophantine Equations. Cambridge University Press, Cambridge (1986)CrossRefMATHGoogle Scholar

Copyright information

© SpringerNature 2018

Authors and Affiliations

  1. 1.AruppukottaiIndia

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