Approximations, Euclid's Algorithm & Continued Fractions

This article sets some puzzles and describes how Euclid's algorithm and continued fractions are related.

Euclid's Algorithm II

We continue the discussion given in Euclid's Algorithm I, and here we shall discover when an equation of the form ax+by=c has no solutions, and when it has infinitely many solutions.

Solving with Euclid's Algorithm

A java applet that takes you through the steps needed to solve a Diophantine equation of the form Px+Qy=1 using Euclid's algorithm.

The original number is $10000x + y$. What is the new number in terms of $x$ and $y$? Use the information to write down a Diophantine equation.