I am given a couple of statements and asked to show the following:
Given: The GCD IDENTITY says "Given integers a and b (not both zero), there exists integers x and y for which gcd (b,a) = ax+by.
Given: If the gcd(a,m) = 1, then the GCD identity (stated above) guarantees that there exists integers u and v such that 1 = au + mv.
Problem: Show that in this case, [u] is the multiplicative inverse of [a] in
.
That's all the information I'm given. Please explain how I would show this multiplicative inverse. Thanks!