A number N is said to be congruent if there are two integers, x and y, that result in the expressions x² + Ny² and x² – Ny² being perfect squares.

The smallest known congruent number is 5 which satisfies 41² + 5(12²) = 49² and 41² – 5(12²) = 31².

The use of the square of a negative number results in another solution of 2² + 5(1²) = 3² and 2² – 5(1²) = (-1)².