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==There is a unique finite field of characteristic <math>p</math> for each power of a prime number <math>p</math>.==

I don't think that this common truth requires a <nowiki>{{prove}}</nowiki> tag: An field of <math>p^n</math> elements can easily be constructed as an extension of a field with <math>p</math> elements, e.g., <math>\mathbb{Z}_p</math>: just look at the zeroes of <math>x^{p^n}-x \in \mathbb{Z}_p[x]</math> in the algebraic closure <math>\overline{\mathbb{Z}}_p</math> .

This field is unique (up to isomorphism, of course), as the multiplicative group of a finite field is cyclic.

--[[User:BRichtigen|BRichtigen]] 12:06, 5 November 2008 (EST)