# Math Help - Number Theory relatively prime.

1. ## Number Theory relatively prime.

Let a and b be relatively prime numbers. prove that (a+b,a-b) is either 1 or 2.

2. 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 $(a+b, a-b) = (a-b, 2)$. Then you know that the gcd is 2 if a-b is even or 1 if a-b is odd.

3. Originally Posted by JCIR
Let a and b be relatively prime numbers. prove that (a+b,a-b) is either 1 or 2.
Hint: $a-b = (a+b) - 2b$.