4. Define GF(8) using arithmetic modulo the irreducible polynomial x3 + x + 1. Write out...

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4. Define GF(8) using arithmetic modulo the irreducible polynomial x3 + x + 1. Write out each of the elements of this field. Compute (x + 1) (x + x) in this field. 5. Define Fg using arithmetic modulo the irreducible polynomial x3 + x + 1. Use Euclid's algorithm to find the gcd(x3 + x + 1, x + 1). Then use Euclid's extended algorithm to find the inverse of x in this field. 4. Define GF(8) using arithmetic modulo the irreducible polynomial x3 + x + 1. Write out each of the elements of this field. Compute (x + 1) (x + x) in this field. 5. Define Fg using arithmetic modulo the irreducible polynomial x3 + x + 1. Use Euclid's algorithm to find the gcd(x3 + x + 1, x + 1). Then use Euclid's extended algorithm to find the inverse of x in this field.