Thilina, On Wed, Jul 3, 2013 at 8:00 AM, Thilina Rathnayake <[email protected]> wrote: > > > > Hi Ondrej, > > I don't know much about solving recurrence relations on two variables, but > the sources > I am referencing provides the solutions for the recurrences involved with > Pell equation. > So, I think that would be enough.
Absolutely. > > Concerning the solutions of x**2 - 13*y**2 = 27, solutions returned by > diop_pell > are: >>>> diop_pell(13, 27) > [(220, 61), (40, 11), (768, 213), (12, 3)] > > Here is how wolfram alpha represents it: > http://www.wolframalpha.com/input/?i=x**2+-+13*y^2+%3D+27 > > They provide general solutions for each class. > (Look in the box named "Integer solutions") It has 4 solutions, the first one is: x = ±1/2 (-40 (649-180 sqrt(13))^n+11 sqrt(13) (649-180 sqrt(13))^n-40 (649+180 sqrt(13))^n-11 sqrt(13) (649+180 sqrt(13))^n), y = ±1/26 (-143 (649-180 sqrt(13))^n+40 sqrt(13) (649-180 sqrt(13))^n-143 (649+180 sqrt(13))^n-40 sqrt(13) (649+180 sqrt(13))^n), n element Z, n>=0 How is this solution mapped to one of the numbers in [(220, 61), (40, 11), (768, 213), (12, 3)] ? Ondrej -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out.
