PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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