1. The problem statement, all variables and given/known data Show that gcd(a+b,a-b) is either 1 or 2. (hint, show that d|2a and d|2b) 2. Relevant equations d = x(a+b)+y(a-b) 3. The attempt at a solution so by the definition of divisibility: a+b = dr a-b = ds adding and subtracting these equalities from eachother 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.