Diophantus again; not to say Pell.

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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.