I came across an interesting problem that I have made no progress on.(adsbygoogle = window.adsbygoogle || []).push({});

Let f be an analytic function on the disc ##D = \{z \in C ~|~ |z| < 1\}## satisfying ##f(0) = 1##. Is the following

statement true or false? If ##f(a) = f^\prime(a) ## whenever ##\frac{1+a}{a}## and ##\frac{1-a}{a}## are prime numbers then ##f(z) = e^z## for all ## z \in D##.

Obviously I know that ##f(z) = e^z## solves ##f^\prime = f##, but I don't see how to use that here.

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# Complex Analysis problem

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