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Smooth values of polynomials | | Jonathan Bober
; Dan Fretwell
; Greg Martin
; Trevor D. Wooley
; | | Date: |
5 Oct 2017 | | Abstract: | Given $fin mathbb{Z}[t]$ of positive degree, we investigate the existence
of auxiliary polynomials $gin mathbb{Z}[t]$ for which $f(g(t))$ factors as a
product of polynomials of small relative degree. One consequence of this work
shows that for any quadratic polynomial $finmathbb{Z}[t]$ and any $epsilon >
0$, there are infinitely many $ninmathbb{N}$ for which the largest prime
factor of $f(n)$ is no larger than $n^{epsilon}$. | | Source: | arXiv, 1710.1970 | | Services: | Forum | Review | PDF | Favorites | |
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