Home

(a) Let $f$ be an entire function such that there exist real constants $M$ and $N$ such that $|f(z)|< M|z|+N$ for all $z$. Prove that for any three pairwise different complex numbers $a,b,c$,$$\frac{f(a)}{(a-b)(a-c)}+\frac{f(b)}{(b-a)(b-c)}+\frac{f(c)}{(c-a)(c-b)}=0$$
(b) Deduce that there are constants $A,B\in\mathbb{C}$ such that $f(z)=Az+B$ for all $z$.