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Suppose B=B(0,R) be a ball in C^n, n>1. Let f be holomorphic in B and continuous on B closure. If f(a)=0 for some a in B, show that there is p in boundary of B such that f(p)=0.

I assumed f(p) is non zero for every point p in boundary B and create contradiction but I can't. Please give me some hints.