Siegel identity

Template:Short description In mathematics, Siegel's identity refers to one of two formulae that are used in the resolution of Diophantine equations.

Statement

The first formula is

\frac{x_{3} - x_{1}}{x_{2} - x_{1}} + \frac{x_{2} - x_{3}}{x_{2} - x_{1}} = 1 .

The second is

\frac{x_{3} - x_{1}}{x_{2} - x_{1}} \cdot \frac{t - x_{2}}{t - x_{3}} + \frac{x_{2} - x_{3}}{x_{2} - x_{1}} \cdot \frac{t - x_{1}}{t - x_{3}} = 1 .

The identities are used in translating Diophantine problems connected with integral points on hyperelliptic curves into S-unit equations.