Smooth values of polynomials

Jonathan Bober, Dan Fretwell, Greg Martin, Trevor Wooley

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

Given of positive degree, we investigate the existence of auxiliary polynomials for which factors as a product of polynomials of small relative degree. One consequence of this work shows that for any quadratic polynomial and any 0$]]>, there are infinitely many for which the largest prime factor of is no larger than.

Original languageEnglish
Pages (from-to)245-261
Number of pages17
JournalJournal of the Australian Mathematical Society
Volume108
Issue number2
Early online date1 Feb 2019
DOIs
Publication statusE-pub ahead of print - 1 Feb 2019

Keywords

  • Smooth numbers
  • polynomials
  • small degree irreducible factors

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