# Difference between revisions of "Euler's phi function"

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=== Identities === | === Identities === | ||

− | For [[prime]] p, <math>\phi(p)=p-1</math>, because all numbers less than p are relatively prime to it. | + | For [[prime]] p, <math>\phi(p)=p-1</math>, because all numbers less than <math>{p}</math> are relatively prime to it. |

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+ | For relatively prime <math>{a}, {b}</math>, <math> \phi{(a)}\phi{(b)} = \phi{(ab)} </math>. | ||

=== Other Names === | === Other Names === |

## Revision as of 12:46, 18 June 2006

**Euler's phi function** determines the number of integers less than a given positive integer that are relatively prime to that integer.

### Formulas

Given the prime factorization of , then one formula for is:

### Identities

For prime p, , because all numbers less than are relatively prime to it.

For relatively prime , .

### Other Names

- Totient Function
- Euler's Totient Function