Changes

:<math>\varphi \left( p_1^{k_1} \cdots p_n^{k_n} \right) = (p_1-1)p_1^{k_1-1} \cdot \cdots \cdot (p_n-1)p_n^{k_n-1}</math>.

:<math>\varphi \left( p_1^{k_1} \cdots p_n^{k_n} \right) = (p_1-1)p_1^{k_1-1} \cdot \cdots \cdot (p_n-1)p_n^{k_n-1}</math>.

=== Some properties of the totient function ===

== Some properties of the totient function ==

* For a prime number <math>p</math>, all numbers less than <math>p</math> are coprime to it, so <math>\varphi(p) = p -1</math>.

* For a prime number <math>p</math>, all numbers less than <math>p</math> are coprime to it, so <math>\varphi(p) = p -1</math>.

* For every <math>n</math>, <math>\varphi(n) \leq n-1</math>.  This is because there are only <math>n-1</math> numbers less than <math>n</math>.

* For every <math>n</math>, <math>\varphi(n) \leq n-1</math>.  This is because there are only <math>n-1</math> numbers less than <math>n</math>.