Let a and b be relatively prime numbers. prove that (a+b,a-b) is either 1 or 2.
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Originally Posted by JCIR Let a and b be relatively prime numbers. prove that (a+b,a-b) is either 1 or 2. Use the gcd algorithm to obtain $\displaystyle (a+b, a-b) = (a-b, 2)$. Then you know that the gcd is 2 if a-b is even or 1 if a-b is odd.
Originally Posted by JCIR Let a and b be relatively prime numbers. prove that (a+b,a-b) is either 1 or 2. Hint: $\displaystyle a-b = (a+b) - 2b$.
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