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Lethbridge Number Theory and Combinatorics Seminar
Date:
January 21, 2019
Time:
12:00 - 12:50 p.m.
Lecturer(s):
Amir Akbary (University of Lethbridge)
Location:
University of Lethbridge
Topic:
Ambiguous Solutions of a Pell Equation
Description:
It is known that if the negative Pell equation X^2 - DY^2 = -1 is solvable (in integers), then all of its solutions can be obtained in a straightforward way from the solution (x, y) with smallest positive x and y. Furthermore, a theorem of Walker from 1967 states that if the equation aX^2 - bY^2 = ±1 is solvable, then all of its solutions can also be obtained in a straightforward way from the solution (x, y) with smallest positive x and y. We describe a unifying theorem that includes both of these results as special cases. The key observation is a structural theorem for the non-trivial ambiguous classes of the solutions of Pell equations X^2 - DY^2 = ±N. This talk is based on the work of Forrest Francis in an NSERC USRA project in summer 2015.
Other Information:
Location: D631 University Hall
Web page: http://www.cs.uleth.ca/~nathanng/ntcoseminar/
Contact:
Barb Hodgson | hodgsonb@uleth.ca | (403) 329-2470 | uleth.ca/artsci/math-computer-science
