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On the Diophantine equation \({y^{p} = \frac{f(x)}{g(x)}}\)

  • S. Subburam
  • A. Togbé
Article
  • 5 Downloads

Abstract

We consider the Diophantine equation
$$y^{p} = \frac{f(x)}{g(x)},$$
where \({x \in \mathbb{Z}}\) and \({y \in \mathbb{Q}}\) are unknowns, f(x) and g(x) are non-zero integer polynomials in variable x and p is prime. We give bounds for x, when \({(x, y) \in \mathbb{Z} \times \mathbb{Q}}\) is a solution of the equation. This improves the results of some recent papers.

Key words and phrases

Diophantine equation monic polynomial 

Mathematics Subject Classification

11D41 11D45 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Department of MathematicsKalasalingam Academy of Research and EducationVirudhunagar DistrictIndia
  2. 2.Department of Mathematics, Statistics, and Computer SciencePurdue University NorthwestWestvilleUSA

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