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Is there a way to solve the second degree Diophantine equation in two variables $ax^{2} -ny^{2} = b$ $(1)$ where a and b are known and n is a parameter; all solutions x= f(n) and y = f(n) ? For example take a =1 and b =1 and solve (1) over the integers, with solutions function of n.

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As usual you can write down all rational solutions if you have one. If you should want integral solutions, the class group will make itself heard. –  franz lemmermeyer Jan 28 '13 at 15:48

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