if a and b are positive integers, show that gcd(a,b)=gcd(a,a+b), gcd represents the greatest common divisor.
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Hello, Originally Posted by tryitall34567 if a and b are positive integers, show that gcd(a,b)=gcd(a,a+b), gcd represents the greatest common divisor. Let d=gcd(a,b) Let d'=gcd(a,a+b) d divides a and b. Hence it divides a+b too. So it divides both a & a+b. Then d divides d'. d' divides a and a+b. Hence it divides (a+b)-a=b. So it divides a & b. Then d' divides d. This shows that d=d'.
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