Cubes in products of terms from an arithmetic progression
Volume 184 / 2018
Acta Arithmetica 184 (2018), 117-126
MSC: Primary 11D61.
DOI: 10.4064/aa8655-5-2017
Published online: 14 May 2018
Abstract
We show that there are no cubes in a product with at least \epsilon \gt 0, terms from a set of k (\geq 2) successive terms in an arithmetic progression having common difference d if either k is sufficiently large or 3^{\omega(d)}\gg k \frac{\log\log k}{\log k}. Here \omega(d) denotes the number of distinct prime divisors of d. This result improves an earlier result of Shorey and Tijdeman.
