Michael A. Bennett

activity

20142023

most citedLong paths in the distance graph over large subsets of vector spaces over finite fields

2 citations · 2 across the 3 of their papers we have counts for

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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.NT2016

Squares with three nonzero digits

Michael A. Bennett, Adrian-Maria Scheerer

We determine all integers $n$ such that $n^{2}$ has at most three base- $q$ digits for $q \in {2, 3, 4, 5, 8, 16}$ . More generally, we show that all solutions to equations of the s…

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

Arithmetic Progressions in Squarefull Numbers

Squares with three nonzero digits

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