Congruent Numbers and Class Groups of Associated Quadratic Fields

In this article, we first discuss congruent numbers and certain recent results concerning their generalizations. Then we review some recent results concerning the 2-part of the class group of \(\mathbb {Q}(\sqrt{\pm n})\) for a congruent number n. We conclude with a sufficient congruence condition for a prime p so that 2p is non-congruent.