M. Bennett

activity

20022023

most citedMordell's equation : a classical approach

14 citations · 51 across the 17 of their papers we have counts for

collaborators

25 papers

math.NT2023

Effective $S$ -unit Equations Beyond 3 Terms : Newman's Conjecture

Prajeet Bajpai, Michael A. Bennett

We show how to effectively solve 5-term $S$ -unit equations when the set of primes $S$ has cardinality at most 3, and use this to provide an explicit answer to an old question of D.…

math.NT2023

Arithmetic Progressions in Squarefull Numbers

Prajeet Bajpai, Michael A. Bennett, Tsz Ho Chan

We answer a number of questions of Erdős on the existence of arithmetic progressions in $k$ -full numbers (i.e. integers with the property that every prime divisor necessarily occur…

math.NT2021★ 8 cited

Differences between perfect powers : prime power gaps

Michael A. Bennett, S. Siksek

We develop machinery to explicitly determine, in many instances, when the difference $x^{2} - y^{n}$ is divisible only by powers of a given fixed prime. This combines a wide variety of t…

math.NT2021

Multidimensional Padé approximation of binomial functions: Equalities

Michael A. Bennett, Greg Martin, Kevin O'Bryant

Let $ω_{0}, \dots, ω_{M}$ be complex numbers. If $H_{0}, \dots, H_{M}$ are polynomials of degree at most $ρ_{0}, \dots, ρ_{M}$ , and $G (z) = \sum_{m = 0}^{M} H_{m} (z) (1 - z)^{ω_{m}}$ has a zero at $z = 0$ of max…

math.NT2021★ 1 cited

Differences between perfect powers : the Lebesgue-Nagell Equation

Michael A. Bennett, Samir Siksek

We develop a variety of new techniques to treat Diophantine equations of the shape $x^{2} + D = y^{n}$ , based upon bounds for linear forms in $p$ -adic and complex logarithms, the modulari…