which is the best proof to use for gcd(a, b) = gcd(a, b − a)

Question

Prove that gcd(a, b) = gcd(a, b − a)

What is the best way to prove this? using induction? or does there exist a more efficient method?

See this answer for the essence of the matter. – Bill Dubuque Dec 01 '15 at 16:01 — Bill Dubuque, Dec 01 '15 at 16:01

Bernard · Answer 1 · 2015-11-20T16:16:11.963

6

The shortest method consists in proving a more general fact: $$\{\text{divisors of }a \text{ and }b\}=\{\text{divisors of }a \text{ and }b-a\}$$

edited Nov 20 '15 at 16:16

answered Nov 20 '15 at 15:44

Bernard

1 Answers1