# Irreducible polynomials mod 2

**Number Theory**Level 5

Let \( {\mathbb F}_2[x] \) be the ring of polynomials with coefficients in \( {\mathbb F}_2 = {\mathbb Z}/2{\mathbb Z} \). Recall that a polynomial is **irreducible** if it has no nonconstant factors of smaller degree.

For example, there are three irreducible polynomials of degree \( 4 \) in \( {\mathbb F}_2[x] \), namely \[ x^4+x+1, x^4+x^3+1, x^4+x^3+x^2+x+1. \]

How many irreducible polynomials of degree 17 are there in \( {\mathbb F}_2[x]?\)