A positive integer is a congruent number when it is the area of a right triangle with rational side lengths. For square-free , this is equivalent to the congruent number elliptic curve having a Mordell-Weil group of positive rank.
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A congruent number is a natural number that is the area of a right triangle with rational number side lengths. In other words, a positive integer \( n \) is called a congruent number if there exists a right triangle with legs of rational lengths such that the area of the triangle is equal to \( n \).