Euler's Totient Function

 N:

Output: `Press calculate`

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Formula:`φ(n)`

Introduction to Euler's Totient Function

Euler's Totient Function, denoted as φ(n), gives the count of positive integers that are coprime to the input number n. Two numbers are said to be coprime if they share no common positive factors other than 1.

Mathematical Background:

Euler's Totient Function is defined as φ(n) = n * (1 - 1/p1) * (1 - 1/p2) * ... * (1 - 1/pk), where p1, p2, ..., pk are the distinct prime factors of n.

Parameter usage:

• `n` = the input number

Output:

• `φ(n)` = count of positive integers coprime to n

Data validation

The number should be greater than zero.

Practical Applications:

Euler's Totient Function has applications in number theory, cryptography, and algorithms such as RSA encryption.

Summary

This function allows the calculation of the count of positive integers coprime to a given number, helping in various mathematical and computational applications.