Ciro Santilli tried to add this example to Wikipedia, but it was reverted, so here we are, see also: Section "Deletionism on Wikipedia".
This is a good first example of a field of a finite field of non-prime order, this one is a prime power order instead.
, so one way to represent the elements of the field will be the to use the 4 polynomials of degree 1 over GF(2):
Note that we refer in this definition to anther field, but that is fine, because we only refer to fields of prime order such as GF(2), because we are dealing with prime powers only. And we have already defined fields of prime order easily previously with modular arithmetic.
Without modulo, that would not be one of the elements of the field anymore due to the !
So we take the modulo, we note that:and by the definition of modulo:which is the final result of the multiplication.
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