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
Most introductory books on number theory have at least one section on the theory of continued fractions. I suggest
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William Stein. Elementary number theory: primes, congruences, and secrets.
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