CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Publicationsjournals
Publications        
Search results

Search: MSC category 11D59 ( Thue-Mahler equations )

  Expand all        Collapse all Results 1 - 1 of 1

1. CJM 2008 (vol 60 pp. 491)

Bugeaud, Yann; Mignotte, Maurice; Siksek, Samir
A Multi-Frey Approach to Some Multi-Parameter Families of Diophantine Equations
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
Categories:11F80, 11D61, 11D59, 11J86, 11Y50

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