Euler's Totient Function
Definition
Basic Values
, , , , ,
Prime Values
Prime Powers
Multiplicative Property
General Formula
where the product is over distinct prime factors of .
Example
Euler's Theorem
Fermat's Little Theorem (Special Case)
When is prime: (since ).
Sum Property
Inverse Totient Problem
Cryptographic Applications
Carmichael Function
Table of Values
| 1 | 1 |
| 2 | 1 |
| 3 | 2 |
| 4 | 2 |
| 5 | 4 |
| 6 | 2 |
| 7 | 6 |
| 8 | 4 |
| 9 | 6 |
| 10 | 4 |
Growth Rate
where is the Euler-Mascheroni constant.