Factoring large numbers is a time-consuming problem. RSA cryptography, and secure communication over the internet, depends on this fact. Algorithms for factoring numbers are also fascinating in their own right. 557 more words

## Tags » Continued Fraction

#### Expmath2 - Ascending continued fractions - part 2

How to write zeta function as an ascending continued fraction? You can find the answer in the fourth paragraph.

Note that it’s similar to Gaussian summation. 277 more words

#### Expmath2 – Generalized continued fractions

How can we interpret this iteration to get the next continued fraction?

I denote the number of iterations with . 219 more words

#### Analysis - Some remarks on continued fractions

Most introductory books on number theory have at least one section on the theory of continued fractions. I suggest

394 more wordsWilliam Stein.

Elementary number theory: primes, congruences, and secrets.

#### Fibonacci numbers, 4

In the preceding post in this series, we saw a connection between the Fibonacci numbers and the golden ratio α = (1+√5)/2. I am going to look at this from a different perspective, that of continued fractions. 1,294 more words

#### Rounding errors

Something has happened to calculators while I wasn’t using them. I am hoping somebody reading this will know more about it than I do.

The story begins with the number theory course I am teaching this year, and a link-up between continued fractions (which form a significant part of the course), Euclid’s algorithm, and the Pythagorean proof of the irrationality of √2. 660 more words

#### 596 - Continued fractions

This term, Summer Hansen is taking a reading course with me on Pell’s equation. Our basic reference is:

- Jacobson and Williams,
**Solving the Pell equation…** 1,240 more words