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Publications Influence

Ternary Diophantine Equations via Galois Representations and Modular Forms

- M. Bennett, C. M. Skinner
- Mathematics
- 1 February 2004

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… Expand

159 17- PDF

Applications of the Hypergeometric Method to the Generalized Ramanujan-Nagell Equation

- M. Bauer, M. Bennett
- Mathematics
- 1 June 2002

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… Expand

54 12- PDF

Rational approximation to algebraic numbers of small height: the Diophantine equation |axn - byn|= 1

- M. Bennett
- Mathematics
- 29 January 2001

Following an approach originally due to Mahler and sharpened by Chudnovsky, we develop an explicit version of the multi-dimensional ``hypergeometric method'' for rational and algebraic approximation… Expand

78 9- PDF

Powers from Products of Consecutive Terms in Arithmetic Progression

- M. Bennett, N. Bruin, K. Gyory, L. Hajdu
- Mathematics
- 1 March 2006

We show that if $k$ is a positive integer, then there are, under certain technical hypotheses, only finitely many coprime positive $k$-term arithmetic progressions whose product is a perfect power.… Expand

41 9- PDF

On the Diophantine equation

- M. Bennett, K. Győry, Á. Pintér
- Mathematics
- 2004

308 7

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

- M. Bennett, V. Vatsal, S. Yazdani
- Mathematics
- 1 November 2004

In this paper, we develop machinery to solve ternary Diophantine equations of the shape Axn + Byn = Cz3 for various choices of coefficients (A,B, C). As a byproduct of this, we show, if p is prime,… Expand

42 5- PDF

Fractional parts of powers of rational numbers

- M. Bennett
- Mathematics
- 1 September 1993

The author uses Pade approximation techniques and an elementary lemma on primes dividing binomial coefficients to sharpen a theorem of F. Beukers on fractional parts of powers of rationals. In… Expand

18 4

On the Diophantine Equation 1

In this paper, we resolve a conjecture of Schäffer on the solvability of Diophantine equations of the shape 1 k + 2 k + · · · + x k = y n , for 1 ≤ k ≤ 11. Our method, which may, with a modicum of… Expand

24 3- PDF

Lucas' square pyramid problem revisited

- M. Bennett
- Mathematics
- 2002

are given by (s, t) = (1, 1) and (24, 70). Putative solutions by Moret-Blanc [30] and Lucas [25] contain fatal flaws (see e.g. [39] for details) and it was not until 1918 that Watson [39] was able to… Expand

13 3- PDF

The representation of integers by binary additive forms

- M. Bennett, N. Dummigan, T. Wooley
- Mathematics
- 1 March 1998

Let a, b and n be integers with ≥ 3. We show that, in the sense of natural density, almost all integers represented by the binary form axn − byn are thus represented essentially uniquely. By… Expand

10 3- PDF