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)?
Solving equations using continued fractions?
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diophantine-equations
continued-fractions
1 Answers
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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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0Sounds great but I couldn't find this book. – 2010-12-16
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0@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. – 2010-12-16