Greatest Common Divisor Theorem

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).

REFERENCES:

Eynden, C. V. Elementary Number Theory, 2nd ed. New York: McGraw-Hill, 2001.

Johnson, P. B. "A Construction of Regular Polygons of  Sides Leading to a Geometric Proof of ." Math. Mag. 38, 164-165, 1965.