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Question

When constructing the finite field with `p^2` elements as `F = ZZ_p[x]"/"langle f(x) rangle`, where f(x) is an irreducible polynomial of degree 2 over `ZZ_p`, what is the nature of the elements in this field F:
A) The elements of F can be uniquely represented by polynomials in `ZZ_p[x]` of degree greater than or equal to 2.
B) The elements of F can be uniquely represented by polynomials in `ZZ_p[x]` of degree at most 1 ?