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<title>CGI-BIN Number Theory Utilities Description</title> |
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<p align="center"><b><font size="4">CGI-BIN Number Theory Utilities Description</font></b></p> |
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<p><a href="http://mathworld.wolfram.com/NumberTheory.html">Number theory</a> is |
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the study of whole numbers and their properties. (<i>Number theory</i> is |
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sometimes also described as the study of integers and integer fields, an |
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equivalent definition.) Notions such as <a href="http://mathworld.wolfram.com/PrimeNumber.html">prime</a> |
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and <a href="http://mathworld.wolfram.com/CompositeNumber.html">composite</a> |
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numbers, as well as famous problems such as <a href="http://mathworld.wolfram.com/FermatsLastTheorem.html">Fermat's |
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last theorem</a>, come from number theory. Many famous mathematicians, |
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such as <a href="http://scienceworld.wolfram.com/biography/Gauss.html">Gauss</a> |
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and <a href="http://scienceworld.wolfram.com/biography/Euler.html">Euler</a>, |
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were number theorists or made substantial contributions to number theory.</p> |
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<p>Number theory is pivotally important in the digital age, as the difficulty of |
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factoring a composite which is the product of large primes is the basis for <a href="http://mathworld.wolfram.com/RSAEncryption.html">RSA |
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public-key cryptography</a>. Number theory also sometimes becomes a |
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consideration in embedded control work, as microcontrollers deal most |
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efficiently with integers and ultimately every input and output of a |
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microcontroller is an integer. Number theory sometimes enters into |
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microcontroller arithmetic (rational approximation, for example) or into |
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hardware design (ratiometric conversion in software, for example).</p> |
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<p>All of the CGI-BIN number theory utilities found at this site perform a |
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calculation or a service which has as its basis number theory.</p> |
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<p>Number theory utilities generally require software to work with large |
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integers. All of the CGI-BIN number theory utilities at this site make use |
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of the <a href="http://www.swox.com/gmp">GMP library</a>, a library for dealing |
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with arbitrarily large integers and arbitrary-precision numbers. Computer |
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arithmetic with large integers is not a trivial matter, and much research has |
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been done about how to efficiently multiply, divide, and perform other |
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operations on large integers (for example, <a href="http://mathworld.wolfram.com/KaratsubaMultiplication.html">Karatsuba |
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multiplication</a>). Using the GMP library for a CGI-BIN application also |
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requires some technical savvy, and the details are <a href="../howtos/sourceforge/use_the_gmp.htm">here</a>.</p> |
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<p>Additionally, all source code for the number theory utilities I've placed on |
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the web is available <a href="../howtos/nth_web_gmp_src_code_dist/obtain_all_source.htm">here</a>.</p> |
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<p align="center" style="margin-top: -2; margin-bottom: -1"><font size="1">This |
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web page is maintained by <a href="mailto:dtashley@users.sourceforge.net">David |
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T. Ashley</a>.</font></p> |
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