- #1
teroenza
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Homework Statement
Given that GCD(a,b)=1 , i.e. they are relatively prime, show that the GCD(a+b,a-b) is 1 or 2.
Homework Equations
am+bn=1 , for some integer m,n.
The Attempt at a Solution
I tried using k(a+b)+L(a-b)=1 or 2, but got nowhere. So I said, if d is the common divisor of (a+b,a-b), d divides the sum or difference of the two.
(a+b)+(a-b)=2a
(a+b)-(a-b)=2b
so d divides either if these. 2 is a common factor between the sum and difference, so I initially thought 2 is then a common factor of (a+b,a-b). I have tried inserting numbers and this is incorrect for some pairs. For example (a,b)=(3,2), and correct for others (3,1). I am not seeing how to differentiate these two cases.
Thank you