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Effective $S$-unit equations beyond three terms: Newman’s Conjecture

Volume 214 / 2024

Prajeet Bajpai, Michael A. Bennett Acta Arithmetica 214 (2024), 421-458 MSC: Primary 11D61; Secondary 11D45, 11J76 DOI: 10.4064/aa230725-14-9 Published online: 21 February 2024

Abstract

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. J. Newman on representations of integers as sums of $S$-units.

Authors

  • Prajeet BajpaiDepartment of Mathematics
    University of British Columbia
    Vancouver, B.C., V6T 1Z2 Canada
    e-mail
  • Michael A. BennettDepartment of Mathematics
    University of British Columbia
    Vancouver, B.C., V6T 1Z2 Canada
    e-mail

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