Advanced Search

We explicitly provide numbers $d$, $e$ such that each irreducible factor of a polynomial $f\left(x\right)$ with integer coefficients has a degree greater than or equal to $d$ and $f\left(x\right)$ can have at most $e$ irreducible factors over the field of rational numbers. Moreover, we prove our result in a more general setup for polynomials with coefficients from the valuation ring of an arbitrary valued field.