Kusniec's Theorem: Demonstrating Prime Numbers Between Squares and the Two Adjacent Oblong Numbers

Important Note (June 2024): A possible critical error has been identified in this version of the preprint. Specifically, the need to use central pairs of complementary divisors was not adequately specified. I am currently reviewing and correcting the manuscript. An updated version will be made available after peer review. I appreciate your understanding and patience. ---------------------------------------------This study aims to provide proof for an extension of Legendre's Conjecture by demonstrating the existence of at least one prime number between a perfect square and its successive oblong number, and vice versa. Specifically, we establish that for any integer n≥1, there is at least one prime p such that n²-n