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No, there is a method to find the convergents.
So I have find the convergent by trial and error
There is a theorem that says that. This is not something I just cooked up, I wished I had.
I have understood everything quite well,but I don't understand what is the logic for taking the convergents,is there any rule for which convergent will be the solution?
Hi Leroy;
Hi again,I have understood pell's equation,now I am curious about nagetive pell's equation,so is there any method to solve x^2ny^2=1
Hi Leroy; With Running the recurrences in the forward direction we get the first bunch:
What ways could you please explain.(sorry for disturbing you so much)
Hi;
You mean every 2nd convergent after the fundamental one?
You use two recurrences to find more answers.
Thank you,now I can find a pell's equation's fundamental solution,but what is the method of finding the additional ones?please explain.
It would seem so. Vardi and others believe he at least formulated the problem correctly even if he was unable to solve for the 205 000 digit answer.
That is interesting, especially how they were only able to get the solution (all the digits) in 1965.
The equation in post #37 is the Pell equation for that problem. 