Publication


Featured researches published by Michael A. Bennett.


Canadian Journal of Mathematics | 2004

Ternary Diophantine Equations via Galois Representations and Modular Forms

Michael A. Bennett; Chris M. Skinner

In this paper, we develop techniques for solving ternary Diophantine equations of the shape Ax n + By n = Cz 2 , based upon the theory of Galois representations and modular forms. We subse- quently utilize these methods to completely solve such equations for various choices of the parameters A, B and C. We conclude with an application of our results to certain classical polynomial-exponential equations, such as those of Ramanujan-Nagell type.


Ramanujan Journal | 2002

Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation

Mark Bauer; Michael A. Bennett

AbstractIn this paper, we refine work of Beukers, applying results from the theory of Padé approximation to (1 − z)1/2 to the problem of restricted rational approximation to quadratic irrationals. As a result, we derive effective lower bounds for rational approximation to


Proceedings of The London Mathematical Society | 2006

Powers from Products of Consecutive Terms in Arithmetic Progression

Michael A. Bennett; Nils Bruin; Kalman Gyory; Lajos Hajdu


Transactions of the American Mathematical Society | 2001

On the representation of unity by binary cubic forms

Michael A. Bennett

\sqrt m


Compositio Mathematica | 2004

Ternary Diophantine equations of signature (p, p, 3)

Michael A. Bennett; Vinayak Vatsal; Soroosh Yazdani


Canadian Journal of Mathematics | 2001

On Some Exponential Equations of S.~S.~Pillai

Michael A. Bennett

(where m is a positive nonsquare integer) by rationals of certain types. Forexample, we have


Bulletin of The London Mathematical Society | 2004

PRODUCTS OF CONSECUTIVE INTEGERS

Michael A. Bennett


International Journal of Number Theory | 2010

THE DIOPHANTINE EQUATION A4 + 2δB2 = Cn

Michael A. Bennett; Jordan S. Ellenberg; Nathan Ng

\left| {\sqrt 2 - \frac{p}{q}} \right| \gg q^{ - 1.47} {\text{ and }}\left| {\sqrt 3 - \frac{p}{q}} \right| \gg q^{ - 1.62}


Journal of The Australian Mathematical Society | 1997

Effective measures of irrationality for certain algebraic numbers

Michael A. Bennett


Compositio Mathematica | 2006

Binomial Thue equations and polynomial powers

Michael A. Bennett; Kalman Gyory; Maurice Mignotte; Ákos Pintér

provided q is a power of 2 or 3, respectively. We then use this approach to obtain sharp bounds for the number of solutions to certain families of polynomial-exponential Diophantine equations. In particular, we answer a question of Beukers on the maximal number of solutions of the equation x2 + D = pn where D is a nonzero integer and p is an odd rational prime, coprime to D.

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