All entire function with $f(\frac{1}{n})=\frac{1}{n^2}$

Question

As you can see in the title I need help with the following exercise:

Find all entire function with $f(\frac{1}{n})=\frac{1}{n^2}$ I guess I have to use the identity theorem but I dont know how

Answer 1

$f(z):=z^2$ will do the job. If $g$ is an entire function with the same property and $h:=f-g$, then $h(1/n)=0$ for all $n$, hence, by the identity theorem: $f=g$ on $ \mathbb C.$