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?
This article sets some puzzles and describes how Euclid's algorithm
and continued fractions are related.
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.
Here is another
beautifully explained solution from Andrei of Tudor Vianu National
College, Bucharest, Romania: