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)?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
Here's how it works:
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
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.