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Let $f:\mathbb{C}\to\mathbb{C}$ be entire function and $g:\mathbb{C}\to\mathbb{C}$ be $g(z)=f(z)-f(z+1)$. Which of the following statements are true?

a. If $f(1/n)=0$ for all positive integers $n$, then $f$ is a constant function.

b. If $f(n)=0$ for all positive integers $n$, then $f$ is a constant function.

c. If $f(1/n)= f(1/n + 1)$ for all positive integers $n$, then $g$ is a constant function.

d. If $f(n)= f(n + 1)$ for all positive integers $n$, then $g$ is a constant function.

I am stuck on this problem. Can anyone help me please?

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    By "positive $n$", do you mean "positive *integers* $n$"?2012-12-17
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    Dear pankaj, you have now asked three questions, all of which show *no* own work. Try investing a little time in the material before you come to us, and if you had any thoughts, please tell us what you've tried.2012-12-17
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    @akkkk Who might "us" be?2012-12-17

3 Answers 3