# 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*^{2} - *h* = *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* = 4*mn*(*m*^{2} - *n*^{2}), where *m* and *n* are integers.