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You are not logged in. #2 20121015 18:08:42
Re: EquationHI Leroy; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20121015 18:13:01
Re: EquationDo you mean integer solutions? It may help if you consider that equation mod 11... #5 20121016 00:05:35
Re: EquationHi Leroy;
If this is your equation then there are no integer solutions. If that  sign in front of the x^2 does not belong there then you are dealing with a Pell equation. This will require continued fractions to understand. Three solutions are (1,0),(10,3) and (199,60). There are infinitely more. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #6 20121018 21:14:16
Re: EquationHow did you find those solutions? I have seen a continued fraction before (such as one for the golden ratio) but how do you use them to find solutions to a Pell equation like Leroy's? #7 20121018 21:26:14
Re: EquationHi zetafunc.; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #9 20121018 21:36:52
Re: EquationHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #10 20121018 21:38:32
Re: EquationThank you. Sorry if it is very long, I am very interested though. #11 20121018 21:44:33
Re: EquationFirst compute the continued fraction of The sequence is periodic with length 2 (6,3...) The nice part is that a theorem by Lagrange assures us that every square root like this will always have a repeating form. Then you get the convergents: You pick the 2nd one ( because the period is 2 ) in the sequence 10/3 and check it in the equation with x = 10 and y = 3 so that is the fundamental solution. x = 10 and y = 3. From there you use two recurrences to get as many as you need. I know you have many questions. This is the prettiest part of number theory. Computational Number Theory! You might want to look at other problems I worked on: http://www.mathisfunforum.com/viewtopic … 12#p115912 post#3. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #12 20121018 22:02:35
Re: EquationThanks for the post. #13 20121018 22:05:02
Re: EquationSee this link and you will know more. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #14 20121018 22:08:32
Re: EquationI read that post, but I am not understanding how you got the sets of repeating forms for √11, √14, √61, etc... sorry if I am missing something obvious. #15 20121018 22:10:09
Re: EquationHi; Repeat steps 2 and 3. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #18 20121018 22:43:56
Re: EquationBut, how can I convince myself that my answer is correct for ? I can see this will get very complicated with further iterations...#19 20121018 22:52:46
Re: Equationc = floor(√11) = 3 ( number you hold ) Now repeat. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #21 20121018 23:09:01
Re: EquationHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #23 20121018 23:16:53
Re: EquationFor the simple one like √11 maybe. But working with symbolic radicals is even harder than working with In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #25 20121018 23:20:45
Re: EquationFor √14 there is an easy theorem to tell you what the fundamental solution is. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 