1.) Let G be a region and let f and g be analytic functions on G such that

f(z)g(z) = 0 on G. Show that either f(z) = 0 or g(z) = 0 on G.

2.) Let f be an entire function with constants 0<M, R>0 and positive integer n>1 such that |f(z)|<M|z|^n for all |z|<R. Prove that f is a polynomial of degree less than or equal to n.