Difference between revisions of "Euler's phi function"

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 $n = p_1^{a_1}p_2^{a_2} \cdots p_n^{a_n}$, then one formula for $\phi(n)$ is: $\phi(n) = n(1-\frac{1}{p_1})(1-\frac{1}{p_2}) \cdots (1-\frac{1}{p_n})$

Identities

For prime p, $\phi(p)=p-1$, because all numbers less than p are relatively prime to it.

Other Names

• Totient Function
• Euler's Totient Function