J. Aust. Math. Soc.  77 (2004), 149-164
On $f(n)$ modulo $\Omega(n)$ and $\omega(n)$ when $f$ is a polynomial

Florian Luca
  Mathematical Institute
  UNAM
  Ap. Postal 61-3 (Xangari)
  CP 58 089 Morelia
  Michoacán
  Mexico
  fluca@matmor.unam.mx


Abstract
In this paper we show that if $f(X)\in \mathbb{Z}[X]$ is a nonzero polynomial, then $\omega(n)|f(n)$ holds only on a set of $n$ of asymptotic density zero, where for a positive integer $n$ the number $\omega(n)$ counts the number of distinct prime factors of  $n$.
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