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A finite field is a field with a finite number of elements. For each prime power $q^k$, there is a unique (up to isomorphism) finite field with $q^k$ elements. Up to isomorphism, these are the only finite fields.

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Polynomials over $\mathbb F_2$ without zeros in $\mathbb F_2$ having an inverse series with ...

If you do not require, $f(1)=1$, then degree 17 and 18 start to beat 2/3, and there is an asymptote, from the data. 6857 t^17 + t^16 + t^2 + 1 6875 t^17 + t^15 + t + 1 7015 t^18 + t^16 + t + 1 6993 t …
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