Required condition for a congruent number: pq with primes p ≡ 1 (mod 8) and q ≡ 3 (mod 8).

In this paper, we establish a crucial requirement for a number of the form n , having two prime factors p and q such that (p , q) ≡ (1 , 3) (mod 8) , to qualify as a congruent number. Specifically, we present congruence relations modulo 16 for the 2-part of the class number of the imaginary quadratic field Q (− 2 p q) when n is congruent. [ABSTRACT FROM AUTHOR]