Solution of the Diophantine equation x² + pᵏ=yⁿ

The main aim of this article is to find all solutions of the Diophantine equation x² + pᵏ=yⁿ where p 1 4, p-13 is a perfect square and the class number of Z-p is 2. In this article, I used a method involving prime factorization and class numbers which is different from using congruent number argument which is widely used in this type of problem.