Suppose we have a polynomial in integer coefficients 

$$p = p_0 + p_1 x + p_2 x^2 + \ldots + p_n x^n, p_k \in \mathbb{Z}$$

Now define $M(p)$ as the maximum absolute value of the coefficients of $p$, i.e.

$$M(p) = \max \{|p_k| \: |\: 0 \leq k \leq n\}$$

Is it true that for any polynomial factor $q$ of $p$, $M(q) \leq M(p)$? I'm not sure whether this is obvious and I'm just missing something, or whether my train of thought is just completely off...


Question: Can I change linenumber colour?
Answer: If you want to change the colour of the line number to blue, then use this in your preamble:   

\renewcommand{\linenumberfont}{\normalfont\bfseries\small\color{blue}}


Full code:

\documentclass{article}
\usepackage{xcolor}
\usepackage{lineno}
\usepackage{lipsum}
\renewcommand{\linenumberfont}{\normalfont\bfseries\small\color{blue}}
\begin{document}
\linenumbers
\lipsum[2-4]
\end{document}