Search for a tool
Euler's Totient

Tool to compute Phi: Euler Totient. Euler's Totient φ(n) is a number representing the number of integers inferior to n, relatively prime with n.

Results

Euler's Totient -

Tag(s) : Mathematics,Arithmetics

dCode and you

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!
You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!


Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Euler's Totient tool. Thank you.

This page is using the new English version of dCode, please make comments !

Euler's Totient

Sponsored ads

This script has been updated, please report any problems.

Euler's Totient Calculator


Display the list of numbers relatively prime with N

Tool to compute Phi: Euler Totient. Euler's Totient φ(n) is a number representing the number of integers inferior to n, relatively prime with n.

Answers to Questions

How to calculate phi(n) (Euler's totient)?

To calculate the value of Euler's Totient, one can realize a prime factorhref decomposition of n.

$$ n=\prod_{i=1}^rp_i^{k_i} $$

With \ (p_i \) prime factorshref and \( k_i \) their number of appearance in decomposition.

You can them apply the formula:

$$ \varphi(n)=\prod_{i=1}^r(p_i-1)p_i^{k_i-1}=n\prod_{i=1}^r\left(1-\frac1{p_i}\right) $$

What is Euler's totient for?

Euler totient function is used in modular arithmetic. It is used in Euler's theorem :

If \( n \) is an integer superior or equal to 1 and \( a \) an integer coprime withhref \( n \), then $$ a^{\phi(n)} \equiv 1 \mod n $$

n=7, a=3 and phi(7) = 6 so 3^6 = 729 = 1 modulo 7href

This theorem is the basis of the RSA encryption.

Ask a new question

Source code

dCode retains ownership of the source code of the script Euler's Totient. Except explicit open source licence (free / freeware), any algorithm, applet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any snippet or function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in PHP (or Java, C#, Python, Javascript, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the Euler's Totient script for offline use, for you, your company or association, see you on contact page !

Questions / Comments


Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Euler's Totient tool. Thank you.


Source : http://www.dcode.fr/euler-totient
© 2016 dCode — The ultimate 'toolkit' website to solve every problem. dCode