Trying to find a particular factor of a polynomial with specific requirements
Ok so I’m trying to prove a result about sicherman dice and I’ve run into a snag
Suppose you have Monic Palindromic polynomial P(x), I would like to find Q(x) such that Q(1) = 1 and Q(x)|P(x) and P(x)/Q(x) has no negative coefficients.
So far I’ve just assumed that Q(x) is of the form 1-x+x^2-x^3+…+x^2n for all natural numbers n but I’ve found some counter examples, I also know it’s probably one cyclotomic polynomial in particular for a given P(x) but I fear it will grow my search space to drastically and if I tried to search through all that it would be too much.