# 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.