If $p \in \mathbb Z[x]$ has non-negative coefficients $\le n$ and if $q$ is a proper divisor of $p$, are the absolute values of the (integer) coefficients of $q$ bounded by some function of $n$; if so, what is a good bound for the case $n=1$?



Factorising single variable polynomials with non-negative integer coefficients
Cyclotomic polynomials divide $p=1+x+\cdots+x^m$ but the (absolute values of) coefficients of cyclotomic polynomials grow unboundedly: see e.g. “ON THE SIZE OF THE COEFFICIENTS OF THE CYCLOTOMIC POLYNOMIAL” by Bateman, available online at <https://www.jstor.org/stable/44165422>


So there is no bound even in the case $n=1$.


