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da/d23/eulers__totient__function_8cpp.html
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<title>Algorithms_in_C++: math/eulers_totient_function.cpp File Reference</title>
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@@ -41,7 +41,7 @@ MathJax.Hub.Config({
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@@ -118,7 +118,8 @@ Functions</h2></td></tr>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >C++ Program to find <a href="https://en.wikipedia.org/wiki/Euler%27s_totient_function" target="_blank">Euler's Totient</a> function. </p>
<p >Euler Totient Function is also known as phi function. </p><p class="formulaDsp">
\[\phi(n) = \phi\left({p_1}^{a_1}\right)\cdot\phi\left({p_2}^{a_2}\right)\ldots\]
\[\phi(n) =
\phi\left({p_1}^{a_1}\right)\cdot\phi\left({p_2}^{a_2}\right)\ldots\]
</p>
<p> where \(p_1\), \(p_2\), \(\ldots\) are prime factors of n. <br />
3 Euler's properties:</p><ol type="1">
@@ -127,7 +128,8 @@ Functions</h2></td></tr>
<li>\(\phi(a,b) = \phi(a)\cdot\phi(b)\) where a and b are relative primes.</li>
</ol>
<p >Applying this 3 properties on the first equation. </p><p class="formulaDsp">
\[\phi(n) = n\cdot\left(1-\frac{1}{p_1}\right)\cdot\left(1-\frac{1}{p_2}\right)\cdots\]
\[\phi(n) =
n\cdot\left(1-\frac{1}{p_1}\right)\cdot\left(1-\frac{1}{p_2}\right)\cdots\]
</p>
<p> where \(p_1\), \(p_2\)... are prime factors. Hence Implementation in \(O\left(\sqrt{n}\right)\). <br />
Some known values are:</p><ul>
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