8. (Finding Multiplicative Inverses Modulo n; The Extended Euclidean Algorithm) Recall that a ∈ Zn has a multiplicative inverse if and only if gcd(a, n) = 1. Moreover, by Theorem 1.4, if gcd(a, n) = 1, then there exist integers r, s ∈ Z so that ar + ns = 1. Reducing modulo n, we have that ar + ns ≡ 1 (mod n). But ns ≡ 0 (mod n), so ar ≡ 1 (mod n). Therefore we may use the Extended Euclidean Algorithm to find the numbers r and s such that ar + ns = 1, and by the above argument, r (reduced modulo n) will be the multiplicative inverse of a in Zn. Using the above argument, find the multiplicative inverse of 14 ∈ Z39.