Tags » Continued Fraction

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

Number Theory

Expmath2 – Generalized continued fractions

Iterations and their continued fraction forms

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

 I denote the number of iterations with . 219 more words

Number Theory

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

William Stein. Elementary number theory: primes, congruences, and secrets.

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414/514: Analysis I

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

Exposition

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

Exposition

596 - Continued fractions

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

Continued Fraction