A positive integer $n$ is given. Consider all polynomials $P(x)=x^n+a_{n-1}x^{n-1}+\ldots+a_0$, whose coefficients are nonnegative integers, not exceeding $100$. Call $P$ reducible if it can be factored into two non-constant polynomials with nonnegative integer coeffiecients, and irreducible otherwise. Prove that the number of irreducible polynomials is at least twice as big as the number of reducible polynomials. D. Zmiaikou