For Algebraic

with , has finitely many solutions. Klaus Roth received a Fields Medal for this result.

**References**

Davenport, H. and Roth, K. F. ``Rational Approximations to Algebraic Numbers.'' *Mathematika* **2**, 160-167, 1955.

Roth, K. F. ``Rational Approximations to Algebraic Numbers.'' *Mathematika* **2**, 1-20, 1955.

Roth, K. F. ``Corrigendum to `Rational Approximations to Algebraic Numbers'.'' *Mathematika* **2**, 168, 1955.

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1999-05-25