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On the Diophantine equation \(x^2-kxy+ y^2 + px = 0\). (Chinese. English summary) Zbl 1363.11050

Summary: Let \(p\) be an odd prime. The author discuss the integer solutions of the equation \(x^2 - kxy + y^2 + px = 0\), and give some necessary conditions of existence of the solutions.

MSC:

11D09 Quadratic and bilinear Diophantine equations