3 papers
math.NT2024
Effective approximation to complex algebraic numbers by quadratic numbers
Prajeet Bajpai, Yann Bugeaud
We establish an effective improvement on the Liouville inequality for approximation to complex non-real algebraic numbers by quadratic complex algebraic numbers.
math.NT2023
Effective -unit Equations Beyond 3 Terms : Newman's Conjecture
Prajeet Bajpai, Michael A. Bennett
We show how to effectively solve 5-term -unit equations when the set of primes 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 -full numbers (i.e. integers with the property that every prime divisor necessarily occur…