| 1 |
dashley |
23 |
<html> |
| 2 |
|
|
|
| 3 |
|
|
<head> |
| 4 |
|
|
<meta http-equiv="Content-Type" content="text/html; charset=windows-1252"> |
| 5 |
|
|
<meta name="GENERATOR" content="Microsoft FrontPage 4.0"> |
| 6 |
|
|
<meta name="ProgId" content="FrontPage.Editor.Document"> |
| 7 |
|
|
<title>CGI-BIN Number Theory Utilities Description</title> |
| 8 |
|
|
<base target="main"> |
| 9 |
|
|
</head> |
| 10 |
|
|
|
| 11 |
|
|
<body background="../bkgnds/bk10.gif"> |
| 12 |
|
|
|
| 13 |
|
|
<p align="center"><b><font size="4">CGI-BIN Number Theory Utilities Description</font></b></p> |
| 14 |
|
|
<hr> |
| 15 |
|
|
<p><a href="http://mathworld.wolfram.com/NumberTheory.html">Number theory</a> is |
| 16 |
|
|
the study of whole numbers and their properties. (<i>Number theory</i> is |
| 17 |
|
|
sometimes also described as the study of integers and integer fields, an |
| 18 |
|
|
equivalent definition.) Notions such as <a href="http://mathworld.wolfram.com/PrimeNumber.html">prime</a> |
| 19 |
|
|
and <a href="http://mathworld.wolfram.com/CompositeNumber.html">composite</a> |
| 20 |
|
|
numbers, as well as famous problems such as <a href="http://mathworld.wolfram.com/FermatsLastTheorem.html">Fermat's |
| 21 |
|
|
last theorem</a>, come from number theory. Many famous mathematicians, |
| 22 |
|
|
such as <a href="http://scienceworld.wolfram.com/biography/Gauss.html">Gauss</a> |
| 23 |
|
|
and <a href="http://scienceworld.wolfram.com/biography/Euler.html">Euler</a>, |
| 24 |
|
|
were number theorists or made substantial contributions to number theory.</p> |
| 25 |
|
|
<p>Number theory is pivotally important in the digital age, as the difficulty of |
| 26 |
|
|
factoring a composite which is the product of large primes is the basis for <a href="http://mathworld.wolfram.com/RSAEncryption.html">RSA |
| 27 |
|
|
public-key cryptography</a>. Number theory also sometimes becomes a |
| 28 |
|
|
consideration in embedded control work, as microcontrollers deal most |
| 29 |
|
|
efficiently with integers and ultimately every input and output of a |
| 30 |
|
|
microcontroller is an integer. Number theory sometimes enters into |
| 31 |
|
|
microcontroller arithmetic (rational approximation, for example) or into |
| 32 |
|
|
hardware design (ratiometric conversion in software, for example).</p> |
| 33 |
|
|
<p>All of the CGI-BIN number theory utilities found at this site perform a |
| 34 |
|
|
calculation or a service which has as its basis number theory.</p> |
| 35 |
|
|
<p>Number theory utilities generally require software to work with large |
| 36 |
|
|
integers. All of the CGI-BIN number theory utilities at this site make use |
| 37 |
|
|
of the <a href="http://www.swox.com/gmp">GMP library</a>, a library for dealing |
| 38 |
|
|
with arbitrarily large integers and arbitrary-precision numbers. Computer |
| 39 |
|
|
arithmetic with large integers is not a trivial matter, and much research has |
| 40 |
|
|
been done about how to efficiently multiply, divide, and perform other |
| 41 |
|
|
operations on large integers (for example, <a href="http://mathworld.wolfram.com/KaratsubaMultiplication.html">Karatsuba |
| 42 |
|
|
multiplication</a>). Using the GMP library for a CGI-BIN application also |
| 43 |
|
|
requires some technical savvy, and the details are <a href="../howtos/sourceforge/use_the_gmp.htm">here</a>.</p> |
| 44 |
|
|
<p>Additionally, all source code for the number theory utilities I've placed on |
| 45 |
|
|
the web is available <a href="../howtos/nth_web_gmp_src_code_dist/obtain_all_source.htm">here</a>.</p> |
| 46 |
|
|
<hr> |
| 47 |
|
|
<p align="center" style="margin-top: -2; margin-bottom: -1"><font size="1">This |
| 48 |
|
|
web page is maintained by <a href="mailto:dtashley@users.sourceforge.net">David |
| 49 |
|
|
T. Ashley</a>.</font></p> |
| 50 |
|
|
<hr noshade size="5"> |
| 51 |
|
|
|
| 52 |
|
|
</body> |
| 53 |
|
|
|
| 54 |
|
|
</html> |
Parent Directory
| 
Revision Log