Publications and Preprints

We show that there are no cubes in a product with at least $k-(1-\epsilon)k\frac{\log\log k}{\log k},\epsilon>0,$ 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.