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Siegel identity

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

Contents

Statement

The first formula is

x 3 − x 1 x 2 − x 1 + x 2 − x 3 x 2 − x 1 = 1.

The second is

x 3 − x 1 x 2 − x 1 ⋅ t − x 2 t − x 3 + x 2 − x 3 x 2 − x 1 ⋅ 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.

References

Siegel identity Wikipedia
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