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On the convergents to a recurring continued fraction, with application to finding integral solutions of the equation ![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20170130102108392-0646:S0013091500034611:S0013091500034611_inline1.gif?pub-status=live)
Published online by Cambridge University Press: 20 January 2009
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1. Let
where D and E are integers, and C a positive integer not a perfect square, k being the number of partial quotients in the non-recurring part of the continued fraction, and c the number in the cycle,
and let
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- Copyright © Edinburgh Mathematical Society 1902