On strings of consecutive integers with no large prime factors

A Balog*, TD Wooley

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

Abstract

We investigate conditions which ensure that systems of binomial polynomials with integer coefficients are simultaneously free of large prime factors. In particular, for each positive number epsilon, we show that there are infinitely many strings of consecutive integers of size about n, free of prime factors exceeding n(epsilon), with the length of the strings tending to infinity with speed log log log log n.

Original languageEnglish
Pages (from-to)266-276
Number of pages11
JournalJournal of the Australian Mathematical Society Series A: Pure Mathematics and Statistics
Volume64
Publication statusPublished - Apr 1998

Keywords

  • smooth numbers
  • consecutive integers
  • sequences

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