There are two different statements, each separately known as the greatest common divisor theorem.
1. Given positive integers 
and 
, it is possible to choose integers 
and 
such that 
, where 
is the greatest
common divisor of 
and 
(Eynden 2001).
2. If 
and 
are relatively prime positive integers, then there exist positive integers 
and 
such that 
(Johnson 1965).
Sides Leading to a Geometric Proof of 
." Math. Mag. 38, 164-165, 1965.