A necessary condition for $2pq$ to be a congruent number

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2025年12月22日

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S. Das

摘要

In this article, we derive a necessary condition for a number of the form n = $2pq$ $2 p q$ , where p and q are distinct prime numbers satisfying $(p, q) \equiv (1, 5) \pmod{8}$ $(p, q) \equiv (1, 5) (mod 8)$ , to be a congruent number. Specifically, we obtain congruence relations involving the 2-part of the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{-pq})$ $Q (\sqrt{- p q})$ , which must hold whenever n is congruent.

A necessary condition for \(2pq\) to be a congruent number

摘要