Introduction to number theory lecture 37 Continued fractions

This lecture is part of my Berkeley math 115 course "Introduction to number theory"
For the other lectures in the course see • Introduction to number...
We show how to used continued fractions to find rationalapproximations to real numbers and to soleve the Pellian equation.
The textbook is "An introduction to the theory of numbers" by Niven, Zuckerman, and Montgomery (5th edition).

[@orthoplex64]

After you mentioned the soldier-based description of x² - 61y² = 1 and its smallest solution in an earlier video, I had to tell my computer to check every lesser positive integer y, because I had such a hard time believing it.

[@migarsormrapophis2755]

yeeeeeeeeeeeeeee

[@oliveryt7168]

Yes.