congruum problem

The congruum problem is to find a square number x 2 such that, when a given number h is added or subtracted, new square numbers are obtained, so that x 2 + h = a 2 and x 2h = b 2. This problem was posed by the mathematicians Théodore and Jean de Palerma in a mathematical tournament organized by Frederick II in Pisa in 1225. The solution is x = m 2 + n 2 and h = 4mn(m 2n 2), where m and n are integers.