# Questions tagged [continued-fractions]

A is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number.

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### Why does this infinite repeating fraction seem to be equal to 2 different values?

Let's start how to find the value of the infinite repeating fraction $$1 + \cfrac{2}{1 + \cfrac{2}{1 + \cdots}}$$ We set the entire expression to $x$, and we notice that the entire expression under ...
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### Hurwitz Test: continued fraction expansion not working

I'm trying to make a Hurwitz fraction expansion of $\;p(s) = s⁴ + s³ + 3s² + 3s +2 \;$ , to check the stability, but can't see what I'm missing. I followed the instructions given in this note, so I ...
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### Cube roots and Continued fractions

I once read that it was not known that for any third degree real number if for its continued fraction (c0; c1, c2, c3, ...) all the iterates are bounded or not. Is this still an open question? I ...
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### A property of the convergents of the continued fraction expansion of a rational number

I'm looking for a proof of the following result (theorem 6.14 of the book Cryptography. Theory and practice by Paterson and Stinson): Theorem 6.14 Suppose that $\text{gcd}(a,b) = \text{gcd}(c,d) = 1$ ...
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Give an example of a perfect set in $\mathbb R$ that does not contain any of the rationals. I found out a proof here using continued fractions. I have trying to understand the proof. In continued ...