I was working out some problems from a entrance test paper, and this problem looked a bit difficult.
- Does there exist an analytic function on $\mathbb{C}$ such that $f\biggl(\frac{1}{2n}\biggr)=f\biggl(\frac{1}{2n+1}\biggr)=\frac{1}{2n} \quad \ \text{for all} \ n\geq 1?$
I did apply $f$ repeatedly to get some more insights about the problem, but couldn't get anything from it. So how do i solve this one?