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

$\frac{x_3-x_1}{x_2-x_1}\cdot \frac{t-x_2}{t-x_3}+\frac{x_2-x_3}{x_2-x_1}\cdot \frac{t-x_1}{t-x_3}=1.$

Application

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

See also

• Siegel formula

References

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