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I found that $x^2+x+1$ is the only polynomial to the power 2 that is irreducible in $z_2$.
Moreover I found that $x^3+x+1$ and $x^3+x^2+1$ are the only polynomials to the power 3 that are irreducible in $z_2$.
Finally I found that that $x^4+x+1$, $x^4+x^2+1$, $x^4+x^2+1$ and $x^4 +x^3+x^2 +x+1$ are the only polynomials to the power 4 that are irreducible in $z_2$.
Hence suppose I want to find an irreducible polynomial, whose largest power is n, in $z_2$. Is there a formula which would let me know how many of these there are?