# Number Theory relatively prime.

• July 9th 2008, 05:33 PM
JCIR
Number Theory relatively prime.
Let a and b be relatively prime numbers. prove that (a+b,a-b) is either 1 or 2.
• July 9th 2008, 05:38 PM
icemanfan
Quote:

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.
• July 9th 2008, 07:04 PM
ThePerfectHacker
Quote:

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

Hint: $a-b = (a+b) - 2b$.