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# Finite Fields and Primitive Elements watch

1. Hello
my question is

Show that =[x] is a primitive element of GF(8)=
I have already worked out that the function in the < > is irreducible but I do not know where to go from this.

2. To be honest, I'm not totally sure what you're supposed to do here. The multiplicative group has 7 elements, which is prime, and so by Lagrange any element other than the identity will generate it.
3. how do you know it has seven elements? sorry, im not very good at this sort of stuff!! i have a vague understanding of lagrange, but do not really know the steps to showing this.

thanks for the reply too
4. The multiplicative group is every element other than 0. Since there are 8 elements total, removing 0 leaves 7 non-zero elements.
5. The elements of GF(8) are the cosets of the possible remainders on division by , right?

How do you know what the possible remainders are though? is there a technique to this??
thanks again
6. The remainders are simply the set of polys of degree < 3.
7. Would they be:

0
1

but i cant think of anymore elements?
would i use just x's?

like:

thanks for your help its much appreciated
8. The remainders are the 8 polys listed above.
9. Thanks !!

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