Recently I mentioned a general method for factoring a large number, not by searching explicitly for factors of the number, but searching instead for congruent squares. 605 more words

## Tags » Continued Fraction

#### Expmath2 - Möbius transformation

Möbius transformation is an interesting definition I came across while I was examining the continued fraction below. I’ve mentioned it previously here.

#### Factoring large numbers using congruent squares

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

#### 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