Siegel's theorem on integral points

In mathematics, Siegel's theorem on integral points states that a curve of genus greater than zero has only finitely many integral points over any given number field.

The theorem was first proved in 1929 by Carl Ludwig Siegel and was the first major result on Diophantine equations that depended only on the genus and not any special algebraic form of the equations. For g > 1 it was superseded by Faltings's theorem in 1983.