Algorithmic Mathematics

Exercise 5.8. Write down all the invertible elements of Z/(30). Exercise 5.9. Apply the algorithm Inverse to determine whether [27]38 is invertible, and if so, to find its inverse. Exercise 5.10. Let f and g be non zero polynomials in F[2]. Prove that deg(f9) = deg() + deg(9). Exercise 5.11. Suppose that g is a gcd of polynomials a and b in F[z], F a field. Prove that if f is a degree zero polynomial in F[x], then fg is also a gcd of a and b. Exercise 5.12. Let K = Z/(5), b E K[x] and suppose that 2x + x + 3 is a greatest common divisor of a and b. Write down all the greatest common divisors of a and b