For more information about this meeting, contact Robert Vaughan.

Title: | Pythagorean tuples |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | Leonid Vaserstein, Penn State University |

Abstract: |

An integer Pythagorean triple is an integer solution (x, y, z) of the equation
x^2+y^2=z^2.
Some of them were known from ancient times. Euclid gave a formula for them. Based on his formula, we have a polynomial Pythagorean triple , with 3 parameters and integer coefficients, which covers all integer Pythagorean triple up to switching x and y. Switching is necessary, but there is a single Pythagorean triple over integer-valued polynomials which covers all integer Pythagorean triples (Frisch-Vaserstein).
Some time ago I reported that the primitive Pythagorean triples, up to switching x and y, can be covered by a polynomial Pythagorean triple (with integer coefficients). My paper in Annals of Mathematics is published in 2010.
In this talk, I consider Pythagorean n-triples. Instead of the sum of 2 squares on the left-hand side, we will have the sum of n-1 squares |

### Room Reservation Information

Room Number: | MB106 |

Date: | 01 / 27 / 2011 |

Time: | 11:15am - 12:05pm |