# CONGRUENT NUMBERS

An online congruent number definition

A number N is said to be congruent if there are two integers, x and y, that result in the expressions x^{2} + Ny^{2} and x^{2} – Ny^{2} being perfect squares.

The smallest known congruent number is 5 which satisfies 41^{2} + 5(12^{2}) = 49^{2} and 41^{2} – 5(12^{2}) = 31^{2}.

The use of the square of a negative number results in another solution of 2^{2} + 5(1^{2}) = 3^{2} and 2^{2} – 5(1^{2}) = (-1)^{2}.