## ad-bc=1ad-bc=1, w=au+bvw=au+bv and z=cu+dvz=cu+dv. Prove \gcd(u,v) = \gcd (w,z)\gcd(u,v) = \gcd (w,z).

As indicated indicated in the title,I am solving the following problem: If ad-bc=1, w=au+bv and z=cu+dv, prove \gcd(u,v) = \gcd (w,z) So from ad-bc=1 I was able to found out \gcd(a+b,c+d) = 1. From here I’m sort of lost as what to do with w = au + bv and z = cu + dv. … Read more