- #1
PsychonautQQ
- 784
- 10
Homework Statement
Show that gcd(a+b,a-b) is either 1 or 2. (hint, show that d|2a and d|2b)
Homework Equations
d = x(a+b)+y(a-b)
The Attempt at a Solution
so by the definition of divisibility:
a+b = dr
a-b = ds
adding and subtracting these equalities from each other we can arrive at where the hint wanted us to conclude:
(r+s) = 2a/d
(r-s) = 2b/d
Trying to figure out what to do from here, having a hard time using the hint to restrict d to 1 or 2.