The lowest-degree polynomials with non-negative coefficients
  A polynomial $p\in\mathbb{R}[x]$ is a divisor of some polynomial $0\neq f\in\mathbb{R}[x]$ with non-negative coefficients if and only if $p$ does not have a positive real root. The lowest possible degree of such $f$ for a given $p$ is known for quadratic polynomials. We provide it for cubic polynomials and improve known bounds of this value for a general polynomial. 
Tom\'a\v{s} Kepka, Miroslav Korbel\'a\v{r}
math.OC math.AC