CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

A Multi-Frey Approach to Some Multi-Parameter Families of Diophantine Equations

  Published:2008-06-01
 Printed: Jun 2008
  • Yann Bugeaud
  • Maurice Mignotte
  • Samir Siksek
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

We solve several multi-parameter families of binomial Thue equations of arbitrary degree; for example, we solve the equation \[ 5^u x^n-2^r 3^s y^n= \pm 1, \] in non-zero integers $x$, $y$ and positive integers $u$, $r$, $s$ and $n \geq 3$. Our approach uses several Frey curves simultaneously, Galois representations and level-lowering, new lower bounds for linear forms in $3$ logarithms due to Mignotte and a famous theorem of Bennett on binomial Thue equations.
Keywords: Diophantine equations, Frey curves, level-lowering, linear forms in logarithms, Thue equation Diophantine equations, Frey curves, level-lowering, linear forms in logarithms, Thue equation
MSC Classifications: 11F80, 11D61, 11D59, 11J86, 11Y50 show english descriptions Galois representations
Exponential equations
Thue-Mahler equations
Linear forms in logarithms; Baker's method
Computer solution of Diophantine equations
11F80 - Galois representations
11D61 - Exponential equations
11D59 - Thue-Mahler equations
11J86 - Linear forms in logarithms; Baker's method
11Y50 - Computer solution of Diophantine equations
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/