Polya showed that there is not much between polynomials and 2^z(roughly speaking), we can also prove that Integer-valued functions can be polynomials if they grow exponentially under some certain condition. In this talk, I will introduce the original result from Polya without details of the proof. And then describe the weaker version of it with full proof. After that, I will say something about some advanced results from my work, which expand the previous result to o-minimal expansion of the ordered field of real numbers. If time allows, I want to introduce a related conjecture made by Alex Wilkie. I won't say any deep concepts in logic, just some tricks in number theory and complex analysis. Everyone can have fun.