Arithmetic Properties of Blocks of Consecutive Integers

Tarlok N. Shorey () and Rob Tijdeman ()
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Tarlok N. Shorey: Indian Institute of Technology
Rob Tijdeman: Leiden University, Mathematical Institute

A chapter in From Arithmetic to Zeta-Functions, 2016, pp 455-471 from Springer

Abstract: 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 ≥ 3.

Keywords: Block of integers; Greatest prime factor; Greatest squarefree divisor; Number of prime factors; Powerfree part; Primary 11A51; Secondary 11D41 (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-28203-9_27

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DOI: 10.1007/978-3-319-28203-9_27

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