<?xml version="1.0" encoding="utf-8" ?> <!-- for emacs: -*- coding: utf-8 -*- -->
<!-- Apache may like this line in the file .htaccess: AddCharset utf-8 .html -->
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" >
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head><title>powermod -- powers of integers mod N</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_powers.html">next</a> | <a href="_power.html">previous</a> | <a href="_powers.html">forward</a> | <a href="_power.html">backward</a> | up | <a href="index.html">top</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> | <a href="http://www.math.uiuc.edu/Macaulay2/">Macaulay2 web site</a></div>
</td>
</tr>
</table>
<hr/>
<div><h1>powermod -- powers of integers mod N</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>powermod(x,i,N)</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><tt>x</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li>
<li><span><tt>i</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li>
<li><span><tt>N</tt>, <span>an <a href="___Z__Z.html">integer</a></span></span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><span>an <a href="___Z__Z.html">integer</a></span>, the <tt>i</tt>-th power of <tt>x</tt> modulo <tt>N</tt></span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : powermod(2,3,10)
o1 = 8</pre>
</td></tr>
<tr><td><pre>i2 : powermod(2,4,10)
o2 = 6</pre>
</td></tr>
<tr><td><pre>i3 : powermod(2,30000,100000)
o3 = 9376</pre>
</td></tr>
<tr><td><pre>i4 : powermod(2,30000,100000000000000000000)
o4 = 35833790694215909376</pre>
</td></tr>
<tr><td><pre>i5 : powermod(2,3331333,3331333)
o5 = 2</pre>
</td></tr>
</table>
</div>
</div>
<div class="waystouse"><h2>Ways to use <tt>powermod</tt> :</h2>
<ul><li>powermod(ZZ,ZZ,ZZ)</li>
</ul>
</div>
</div>
</body>
</html>
