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.

If the last four digits of my phone number are placed in front of the remaining three you get one more than twice my number! What is it?

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.

Use Euclid's algorithm to get a rational approximation to the number of major thirds in an octave.

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