# Irreducible polynomials mod 2

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 ${\mathbb F}_2[x]?$

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