Problem:

Show that if ad - bc = 1 or -1, then gcd(a+b, c+d) = 1.

Work so far:

I know that since a(d) + b(-c) = 1 or -1, then the gcd(a,b) = 1. The same can be also said to show gcd(c,d) = 1, gcd(a,c) = 1, and gcd(b,d) = 1. I also know that gcd(a+b, c+d) divides a+b and c+d, so it will divide any linear combination of a+b and c+d.

I'm really at a loss of where to go from here.