Which of the following statements are true?
There exists an entire function $f : \mathbb C\rightarrow \mathbb C$ which takes only real values and is such that $f(0) = 0$ and $f(1) = 1$.
There exists an entire function $f : \mathbb C\rightarrow \mathbb C$ such that $f(n + {1\over n}) = 0$ for all positive integers $n$.
There exists an entire function $f : \mathbb C\rightarrow \mathbb C$ which is onto and which is such that $f({1\over n}) = 0$ for all positive integers $n$.