### Abstract

A polynomial parametrization for the group of integer two-by-two matrices with determinant one is given, solving an old open problem of Skolem and Beurkers. It follows that, for many Diophantine equations, the integer solutions and the primitive solutions admit polynomial parametrizations.

Original language | English (US) |
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Pages (from-to) | 979-1009 |

Number of pages | 31 |

Journal | Annals of Mathematics |

Volume | 171 |

Issue number | 2 |

DOIs | |

State | Published - Jul 6 2010 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

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*Annals of Mathematics*, vol. 171, no. 2, pp. 979-1009. https://doi.org/10.4007/annals.2010.171.979

**Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups.** / Vaserstein, Leonid N.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups

AU - Vaserstein, Leonid N.

PY - 2010/7/6

Y1 - 2010/7/6

N2 - A polynomial parametrization for the group of integer two-by-two matrices with determinant one is given, solving an old open problem of Skolem and Beurkers. It follows that, for many Diophantine equations, the integer solutions and the primitive solutions admit polynomial parametrizations.

AB - A polynomial parametrization for the group of integer two-by-two matrices with determinant one is given, solving an old open problem of Skolem and Beurkers. It follows that, for many Diophantine equations, the integer solutions and the primitive solutions admit polynomial parametrizations.

UR - http://www.scopus.com/inward/record.url?scp=77954152608&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954152608&partnerID=8YFLogxK

U2 - 10.4007/annals.2010.171.979

DO - 10.4007/annals.2010.171.979

M3 - Article

AN - SCOPUS:77954152608

VL - 171

SP - 979

EP - 1009

JO - Annals of Mathematics

JF - Annals of Mathematics

SN - 0003-486X

IS - 2

ER -