Smooth Values of Polynomials

J. W. Bober*, D. Fretwell, G. Martin, T. D. Wooley

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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

Original languageEnglish
Pages (from-to)245-261
Number of pages17
JournalJournal of the Australian Mathematical Society
Issue number2
Early online date1 Feb 2019
Publication statusPublished - 1 Apr 2020
Externally publishedYes


  • polynomials
  • small degree irreducible factors
  • Smooth numbers


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