Diophantus of Alexandria/Arithmetica/Book 3/Problem 6

Example of Diophantine Problem
Let $\set {x, y, z}$ be a set of $3$ natural numbers such that:


 * $x + y + z$ is square
 * $x + y$ is square
 * $y + z$ is square
 * $x + z$ is square.

What are those $3$ numbers?

Solution
The solution given by is:
 * $\set {41, 80, 320}$

As can be seem: