Try this site first:

]]>No bother at all. You remember that the fundamental solution is x = 10 and y = 3. We use that to get all the rest.

With

Running the recurrences in the forward direction we get the first bunch:

]]>Yes, that is one way if you have the convergents. x=numerator and y=denominator of the period.

There are other ways that do not require the convergents.

]]>So, Archimedes probably knew that equations of that form were solvable.

]]>Read this for more:

http://www.sciencenews.org/sn_arc98/4_1 … thland.htm

It took more that 1800 years for someone to partially solve the problem. It was only solved fully in the 20th century with the aid of computers.

Incidentally, the Pell equation is incorrectly named. Pell had nothing to do with it. It should be called Fermat's equation.

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