Lecture 20: Continued Fractions IV:
Applications

William Stein

Date: Math 124 $\quad$ HARVARD UNIVERSITY $\quad$ Fall 2001

In this lecture we will learn about two applications of continued fractions. The first is a solution to the computational problem of recognizing a rational number using a computer. The second application is to the following ancient question: Given a positive nonsquare integer $d$, find integers $x$ and $y$ such that $x^2 - dy^2 = 1$.