Effective $S$-unit equations beyond three terms: Newman’s Conjecture
Volume 214 / 2024
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.
