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?