1. CJM 2010 (vol 63 pp. 136)
2. CJM 2008 (vol 60 pp. 491)
 Bugeaud, Yann; Mignotte, Maurice; Siksek, Samir

A MultiFrey Approach to Some MultiParameter Families of Diophantine Equations
We solve several multiparameter families of binomial Thue equations of arbitrary
degree; for example, we solve the equation
\[
5^u x^n2^r 3^s y^n= \pm 1,
\]
in nonzero integers $x$, $y$ and positive integers $u$, $r$, $s$ and $n \geq 3$.
Our approach uses several Frey curves simultaneously, Galois representations
and levellowering, 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, levellowering, linear forms in logarithms, Thue equation Categories:11F80, 11D61, 11D59, 11J86, 11Y50 

3. CJM 2001 (vol 53 pp. 897)
 Bennett, Michael A.

On Some Exponential Equations of S.~S.~Pillai
In this paper, we establish a number of theorems on the classic
Diophantine equation of S.~S.~Pillai, $a^xb^y=c$, where $a$, $b$ and
$c$ are given nonzero integers with $a,b \geq 2$. In particular, we
obtain the sharp result that there are at most two solutions in
positive integers $x$ and $y$ and deduce a variety of explicit
conditions under which there exists at most a single such solution.
These improve or generalize prior work of Le, Leveque, Pillai, Scott
and Terai. The main tools used include lower bounds for linear forms
in the logarithms of (two) algebraic numbers and various elementary
arguments.
Categories:11D61, 11D45, 11J86 
