Smooth Values of Polynomials

Fretwell, Dan and Wooley, Trevor and Bober, Jonathan and Martin, Greg (2020) Smooth Values of Polynomials. Journal of the Australian Mathematical Society, 108 (2). pp. 245-261. ISSN 1446-7887

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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.

Item Type:
Journal Article
Journal or Publication Title:
Journal of the Australian Mathematical Society
Uncontrolled Keywords:
?? smooth numberspolynomialssmall degree irreducible factorsgeneral mathematicsmathematics(all) ??
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Deposited On:
06 Jul 2023 08:55
Last Modified:
16 Jul 2024 12:04