Is it correct that if there exists coefficients m and n ∈ ℤ such that ma + nb = 1, gcf (a, b) = 1? I assume it's right but I wanted to double check...
Ach! I finally recalled the name of it. You are looking for the Euclidean algorithm, specifically the section on Euclid's lemma.
-Dan
Theorem: ma+nb=1 implies gcd(a,b)=1
Proof:
If d divides a and b, then d divides 1 using basic properties of divisibility and therefore gcd(a,b)=1
conversely,
Given gcd(a,b)=1 there exist integers m,n such that ma+nb=1
to find m and n we can use the division algorithm