This question was simply a result of my misreading the example on page 93, where it says
"We first solve Pell's equation x2 5y2 = 1 with d = 5 by nding the units of the ring of integers of Q(sqrt(5) using Sage." Of course I should have realized that just finding those units will give me the solutions of x^2 - 5 y^2 = plus or minus 1, not just 1. I'm sorry for taking your time to point that out. On Friday, October 31, 2014 9:14:02 AM UTC-7, Michael Beeson wrote: > > Here I attempt to solve Pell's equation with d = 1621 following the method > on page 93 of Stein's book. > But the solution produced is instead a solution of the negative Pell > equation x^2-y^2 = -1 (instead of 1). > Actually, the example on page 93 (after correcting the typo "v" to "u") > has the same problem: it claims > that [-2,1] solves Pell's equation with d=5, whereas, it really solves > the negative Pell equation. > > sage: K.<a> = QuadraticField(1621) > sage: G = K.unit_group() > sage: u = G.1 > sage: L = [list(u^i) for i in [0..3]] > sage: L > [[1, 0], [4823622127875/2, 119806883557/2], [23267330432525342852015627/2, > 577903134597288688851375/2], [56116404965454319198851772383057215250, > 1393793173905903098261469193463230841]] > sage: x = L[2][0]; > sage: y = L[2][1]; > sage: x > 23267330432525342852015627/2 > sage: x = L[3][0]; > sage: y = L[3][1]; > sage: x > 56116404965454319198851772383057215250 > sage: y > 1393793173905903098261469193463230841 > sage: x^2-1621*y^2 > -1 > > > -- You received this message because you are subscribed to the Google Groups "sage-support" 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/sage-support. For more options, visit https://groups.google.com/d/optout.
