Arithmetic properties of blocks of consecutive integers

Abstract

This paper provides a survey of results on the greatest prime factor, the number of distinct prime factors, the greatest squarefree factor and the greatest m-th powerfree part of a block of consecutive integers, both without any assumption and under assumption of the abc-conjecture. Finally we prove that the explicit abc-conjecture implies the Erdős-Woods conjecture for each k>2.

A slightly corrected and extended version of a paper which will appear in January 2017 in the book From Arithmetic to Zeta-functions published by Springer