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Let Z_2 [x] be the ring of all polynomials with coefficients in Z_2. List the elements...

Let Z_2 [x] be the ring of all polynomials with coefficients in Z_2. List the elements of the field Z_2 [x]/〈x^2+x+1〉, and make an addition and multiplication table for the field. For simplicity, denote the coset f(x)+〈x^2+x+1〉 by (f(x)) ̅.

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