Statement to be proved: Assuming that $(a, b) = 2$, prove that $(a + b, a − b) = 1$ or $2$.
I was thinking that $(a,b)=\gcd(a,b)$ and tried to prove the statement above, only to realise that it is not true.
$(6,2)=2$ but $(8,4)=4$, seemingly contradicting the statement to be proved?
Is there any other meaning for $(a,b)$, or is there a typo in the question?
Sincere thanks for any help.