Arithmetic properties of blocks of consecutive integers
Number Theory
2016-12-19 v1
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 Erd\H{o}s-Woods conjecture for each k>2.
Keywords
Cite
@article{arxiv.1612.05438,
title = {Arithmetic properties of blocks of consecutive integers},
author = {Tarlok N. Shorey and Rob Tijdeman},
journal= {arXiv preprint arXiv:1612.05438},
year = {2016}
}
Comments
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