Question: Consider the finite field GF(2^4 ) obtained via arithmetic modulo the irreducible polynomial p(x) = x^4 + x + 1. Find the inverse of f(x)

Consider the finite field GF(2^4 ) obtained via arithmetic modulo the irreducible polynomial p(x) = x^4 + x + 1.

Find the inverse of f(x) = x in GF(2^4 ), i.e. the polynomial g(x) such that f(x)g(x) = 1 in GF(2^4 ).

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