Question

Given gcd(a,b)=1, prove that gcd(a+b,a-b)=1 or 2.

Answer 1

A+b=2 but a-b = 0

Answer 2

ssorry if i am wrong but i am 89% sure this is right

Answer 3

Found the proof in my teacher's ppt.
gcd(a,b)=1
g=gcd(a+b,a-b)
g|a+b and g|a-b
g|a+b+(a-b)=2a and g|a+b-(a-b)=2b
->g|gcd(2a+2b)
->g|2 gcd(a,b)
->g|2
->g=1 or g=2