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Which of the following statements are true?

  1. There exists an entire function $f : \mathbb C\rightarrow \mathbb C$ which takes only real values and is such that $f(0) = 0$ and $f(1) = 1$.

  2. There exists an entire function $f : \mathbb C\rightarrow \mathbb C$ such that $f(n + {1\over n}) = 0$ for all positive integers $n$.

  3. 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 $n$.

  • 1
    What do you mean by $f(n+1n)$?2012-08-02
  • 0
    What have you tried? What relevant facts do you know? (For example, are you familiar with Picard's theorems?)2012-08-02

2 Answers 2