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By considering the norm of elements in the ring of integers in$\mathbb{Q}(\sqrt{-a})$, we give an algebraic approach to count the number ofintegral solutions of diophantine equations of the form $x^2+ay^2=n$ where $a$is a Heegner number or $a=27$.

An algebraic approach to count the number of representations of an integer by the quadratic form $x^2+ay^2$ for certain values of $a$