## congruum problemFind 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 = 4mn(m^{2}
- n^{2}), where m and n are integers.
## Related category• NUMBER THEORY | |||||

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