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 n^2-n