Title: Continued fractions and the Pell equation
Author: Martin Kuděj
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A long time ago, there were dinosaurs. But they didn't solve diophantine equations thus they became extinct. This means that we have to solve them not to suffer the same fate! Let's begin with the Pell equation x^2-Ny^2=+-1 by solving it using a good choice of a rational approximation of the square root of N, which will be found using continued fractions.
Video:

Video (backup): Videosoubor (MP4) Continued fractions and the Pell equation.mp4
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Komentáře

  • TTTereza Tichá - úterý, 18. května 2021, 15.08
    Thank you for your talk and your presentation. I enjoyed it. Could you please explain why N in Pell equation cannot be square? What would happen if it was square?
  • DRDavid Ryzák - středa, 26. května 2021, 20.48
    Thank you for nice and understandable talk. Although I do not do any research in number theory in the moment, I like it , because this field has so many easily understable problems, however problems which are hard to solve. I would like to ask a question about a continued fraction. For squre root of positive integers (which are irational) continued fraction looks like you showed, so there is a_0 and some period of some length. For square root of two there was period of length 1. I would like to ask if something like this statement is true: Period(square root of (a*b))=Period(a)*Period(b), where a and b are for instance prime numbers or any positive integers? By period I mean length of the period in continued fraction of that number.