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?
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See this answer for the essence of the matter. – Bill Dubuque Dec 01 '15 at 16:01
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The shortest method consists in proving a more general fact: $$\{\text{divisors of }a \text{ and }b\}=\{\text{divisors of }a \text{ and }b-a\}$$
Bernard
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