On the Diophantine Equations of the Form \( x^2 - kxy + ky^2 + 2ny = 0 \) (European Journal of Pure and Applied Mathematics, 2025)
In this article, we determine all values of \( k \) for which the equation \( x^2 - kxy + ky^2 + 2ny = 0 \), where \( n = 3,4,5,6,7 \),  has infinitely many positive solutions.
Keywords: Diophantine Equation; Pell Equation; Quadratic Diophantine Equation