To prove that if a is even and b is odd, then gcd(a, b) = gcd(a/2, b), note that because
Chapter 2, Problem 24(choose chapter or problem)
To prove that if a is even and b is odd, then gcd(a, b) = gcd(a/2, b), note that because b is odd, 2 is not a factor of b, hence not a factor of gcd(a, b). Therefore all contribution to gcd(a, b) comes from b and a/2, and gcd(a, b) = gcd(a/2, b). Write an equation for gcd(a, b) when a is odd and b is even.
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