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I'm writing a paper on Pell's equations and found a solution technique for $x^2-61y^2=1$.
At first glance I thought it was the Chakravala method (I'm very new to this topic), but upon further inspection it seems to be something else entirely. Could someone please tell me what method this is and/or give me resources for learning more? screencap of forum posting

Widawensen
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Wrinkly-Butts
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  • I didn't see that the screenshot uses anything from the chakravala-method, but is explained in terms of continued fractions only. That purely continued-fraction-based method is in wikipedia assigned to Lagrange and/or some others (don't know the canonical name) https://en.wikipedia.org/wiki/Chakravala_method – Gottfried Helms Nov 29 '17 at 10:41
  • If you say "the continued algorithm algorithm" in the context of Pell equations people will probably know what you mean. There's an explanation and proof in "An Introduction to the Theory of Numbers" by Hardy and Wright, which happened to have gone into public domain yesterday. – Sophie Dec 02 '17 at 22:55

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