A pawn stands on one of the squares of an endless in both directions chequered strip of paper. It can be shifted by \(m\) squares to the right or by \(n\) squares to the left. For which \(m\) and \(n\) can it move to the next cell to the right?
Prove that the equation \(\frac {x}{y} + \frac {y}{z} + \frac {z}{x} = 1\) is unsolvable using positive integers.
In a room, there are three-legged stools and four-legged chairs. When people sat down on all of these seats, there were 39 legs (human and stool/chair legs) in the room. How many stools are there in the room?