The full question is: Let f be an entire function and L be a lattice in $\mathbb{C}$. For every lattice point $ω \in L$ we assume that there exists a polynomial $P_ω$ such that $f(z+ω)=f(z)+P_ω(z)$ $\forall z \in C$. Show that f itself is a polynomial.
I'm not sure how to approach this. We've tried looking at the power series expansion of f in comparison to that of $P_w$ and didn't get anywhere. Apparently this is a generalization of Liouville's theorem, but I don't know a lot about elliptic functions or lattices, so i can't really draw the connection. Any help would be appreciated.