Diophantus of Alexandria/Arithmetica/Book 1/Problem 22

Example of Diophantine Problem

 * To find $3$ numbers such that, if each give to the next following a given fraction of itself, in order, the results after each has given and taken may be equal.

That is:

Let $\dfrac 1 p, \dfrac 1 q, \dfrac 1 r$ be given.

The exercise is to find a set of $3$ natural numbers $\set {x, y, z}$ such that:

where $m$ is a natural number.