Would you correct me? Which of the following statements are true?
a. There exists an entire function $f : \mathbb{C}\rightarrow\mathbb{C}$ which takes only real values. and is such that $f(0) = 0$ and $f(1) = 1$
b. There exists an entire function $f : \mathbb{C}\rightarrow\mathbb{C}$ such that $f(n + 1/n) = 0$ for all $n\in\mathbb{N}$
c. There exists an entire function $f : \mathbb{C}\rightarrow\mathbb{C}$ which is onto and which is such that $f(1/n) = 0$ for all $n\in\mathbb{N}$
Well, for a) it is only constants.
b) can have such non-constants entire function.
c) only constants.
Are my answers correct?plz help.