Explain how to construct a field of order 343 not using addition and multiplication tables.
I understand that every finite field has order pn for some prime p. Since 343 is 73, let p=7. I believe I need to find a polynomial of degree 3 which does not factor over Z7. I have considered the following polynomial x3+x+1 and showed that it is irreducible over Z7.
I am not sure how to procede from here, any help would be great.
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