I have been reading about some Diophantine equations (like Runge's theorem and Cassel's theorem) and in the text says that these theorems are solved using Runge's method, but it doesn't say what exactly Runge's method is, the things that I see in common are
- A change of variables
- Put a variable depending of the other one (like a power series $f(x)$ and also a polynomial $p(x)$)
- Analyse the coefficients of the polynomial and the power series and put a bound to the power series ($< 1$)
- Note that when the equation holds the polynomial and the power series have the same value, and because of this $p(x) = 0$ and then this implies what we want.
Is this Runge's method? What am I missing? Or am I completely wrong?
Thanks.