Question 48
Given $n \in \mathbb{N}$. Consider polynomials of degree $n$ of the form $P(x) = x^n + a_{n-1}x^{n-1} + \dots + a_1x + a_0$ with non-negative integer coefficients not exceeding $100$. We call such a polynomial *expandable* if it can be represented as a product of two non-constant polynomials with non-negative integer coefficients, and *non-expandable* otherwise. Prove that there are at least twice as many non-expandable polynomials as there are expandable ones.