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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html">math</a></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/d64/namespacemodular__division.html">modular_division</a></td></tr>
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<tr class="memdesc:a66cdf93153cbd1408bd74ac68961d179"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function calculates a raised to exponent b under modulo c using modular exponentiation. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p>An algorithm to divide two numbers under modulo p <a href="https://www.geeksforgeeks.org/modular-division" target="_blank">Modular Division</a> </p>
<p>To calculate division of two numbers under modulo p Modulo operator is not distributive under division, therefore we first have to calculate the inverse of divisor using <a href="https://en.wikipedia.org/wiki/Fermat%27s_little_theorem" target="_blank">Fermat's little theorem</a> Now, we can multiply the dividend with the inverse of divisor and modulo is distributive over multiplication operation. Let, We have 3 numbers a, b, p To compute (a/b)p (a/b)p ≡ (a*(inverse(b)))p ≡ ((ap)*inverse(b)p)p NOTE: For the existence of inverse of 'b', 'b' and 'p' must be coprime For simplicity we take p as prime Time Complexity: O(log(b)) Example: ( 24 / 3 ) % 5 =&gt; 8 % 5 = 3 &mdash; (i) Now the inverse of 3 is 2 (24 * 2) % 5 = (24 % 5) * (2 % 5) = (4 * 2) % 5 = 3 &mdash; (ii) (i) and (ii) are equal hence the answer is correct. </p><dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d8/d53/modular__inverse__fermat__little__theorem_8cpp.html" title="C++ Program to find the modular inverse using Fermat&#39;s Little Theorem">modular_inverse_fermat_little_theorem.cpp</a>, <a class="el" href="../../d0/d6d/modular__exponentiation_8cpp.html" title="C++ Program for Modular Exponentiation Iteratively.">modular_exponentiation.cpp</a> </dd></dl>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/shubhamamsa" target="_blank">Shubham Yadav</a> </dd></dl>
<p class="definition">Definition in file <a class="el" href="../../df/d72/modular__division_8cpp_source.html">modular_division.cpp</a>.</p>
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<p>Function for testing power function. test cases and assert statement. </p><dl class="section return"><dt>Returns</dt><dd><code>void</code> </dd></dl>
<p>Function for testing power function. test cases and assert statement. </p><dl class="section return"><dt>Returns</dt><dd><span class="tt">void</span> </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../df/d72/modular__division_8cpp_source.html#l00089">89</a> of file <a class="el" href="../../df/d72/modular__division_8cpp_source.html">modular_division.cpp</a>.</p>
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