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We solve the pell equation using the continued fraction for square root of 2. What equations can we solve using the continued fraction of cube roots (and other numbers too)?

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Voronoi developed a generalized continued fraction algorithm for computing units in cubic fields. You can find a beautiful geometric interpretation of Voronoi's algorithm in Delone and Faddeev's: Theory of Irrationalities of Third Degree.

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Sounds great but I couldn't find this book. – quanta Dec 16 '10 at 13:04
@quanta: Because that book is the standard reference, Googling the author's names should turn up almost all that has been written on the topic. – Gone Dec 16 '10 at 13:24

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