SUFFICIENT CONDITION FOR NON-CONGRUENT pq AND 2pq WITH PRIMES p AND q IN THE FORM OF 8k + 1

Within this article, our focus lies on positive integers represented as pq and 2pq, where p and q are prime numbers adhering to the conditions p ≡ q ≡ 1 (mod 8). Additionally, we will operate under the assumption that q is a quadratic non-residue modulo p. Our aim is to present a condition that ensures that n is a non-congruent number, and we will substantiate the sufficiency of this condition through proof.

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