The theorem that says that if
m and n are two natural numbers,
it is possible to choose two integers, c and d,
such that
cm + dn is a common factor
Is sometimes called the GCF theorem; that is the Greatest Common Factor
theorem. Does it have other names?
I know that it is fundamental in number theory, and is often used for
relatively prime numbers in which case cm + dn = 1. If follows from the
Euclidean algorithm, but Euclid did not have negatives. Do we know where
it was first stated in print this way?
Best wishes from Annapolis,
Sam Kutler