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In the finite field GF(2 3 )  defined by the irreducible polynomial m(x)  =  ...

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In the finite field GF(23) defined by the irreducible polynomial

m(x)  =  x3+x+1,

find the multiplicative inverse of the polynomial x2+1. In other words, determine the polynomial A(x) such that

(x2+1) A(x)  ≡  1 (mod x3+x+1)

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