Problem 3E

Trace Algorithm 3 when it finds gcd(8,13). That is. show all the steps used by Algorithm 3 to find gcd(8, 13).

Lecture 13 Wednesday, October 26, 2016 10:34 AM Modular Inverse, exponentiation Recall: - Bezout's theorem:If a and b are positive integer, then there exist integers s and t such that gcd(a, b) = sa + tb. A. Multiplicative inverse mod m - Suppose GCD(a, m) = 1 - By Bezout's Theorem,there existsintegers s and t such that sa+tm=1. - S mod m is the multiplicative inverse of a: 1 = (sa + tm) mod m = sa mod m. - Gcd(a, m) = 1 if m is prime and 0 < a < m so can always solve these equations mod a prime. B. Fast Exponentiation a^k mod m for all k.