Talk:Pell's equation

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Mathematics rating:	B Class	High Priority	Field: Number theory
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Needs a more encyclopedic style, I think. Also, is this yet a balanced account of the theory? Geometry guy 22:21, 9 June 2007 (UTC)

<quote> It turns out that if (p, q) satisfies Pell's equation, then so does (2pq, 2q^2-1).</quote>

Does it?

n(2q² − 1)² + 1 = 4nq⁴ − 4nq² + n + 1;4p²q² = 4(nq² + 1)q² = 4nq⁴ + 4q²

Which aren't generally equal. (Probably only for n = -1) --User:Xaos

[edit] Indeterminate equations

I removed the words "quadratic indeterminate" from

"Pell's equation is any quadratic indeterminate Diophantine equation of the form x² − ny² = 1."

because the form already says that the equation is quadratic and indeterminate (in the sense of underdetermined). It is claimed that "there are many scholars referring to Pell's equation as an indeterminate equation", but I've seen no evidence for it and I still doubt that it's a standard term; anyway, it clearly is superfluous. -- Jitse Niesen (talk) 07:49, 10 April 2006 (UTC)

[edit] As motivation...

What is the purpose of this section with the square root of 2, and averaging the two fractions and so on. This method is not detailed like the Indian method or Lagrange's, and it only seems to work with this specific example. It provides no evidence to back the procedure up. Perhaps this section could be clarified, or maybe it should be considered for removal. —The preceding unsigned comment was added by Xcelerate (talk • contribs) 17:18, 15 January 2007 (UTC).

As part of a major reorganization of this article, I removed this section. Like you I found it unhelpful. I replaced it with a more straightforward worked-out example for n = 7, which gives I think a better flavor of the general technique. —David Eppstein 20:09, 20 March 2007 (UTC)

A (partial) solution given by Euler (??) was to write Pell's equation

Nx² − y² = 1 as then for big (x,y) y=m and x=n with m and n the convergents of the continued fraction for —Preceding unsigned comment added by Karl-H (talk • contribs)

I believe the continued fraction solution technique described in the article is due to Euler. Is that what you mean? —David Eppstein 22:58, 24 March 2007 (UTC)

[edit] history

ok, i dont know about the indians, but it was certainly studied before Pell's times. Fermat certainly did. Fermat's theorem on Epll eqn.

16:48, 10 June 2007 (UTC)70.18.52.179 16:48, 10 June 2007 (UTC)