Ford proved a result showing that for each k, the equation this function of x equals m has exactly k solutions. Jordan extended this function to k-tuples. This function appears in the denominator of the definition of the Silverman Constant. The Dirichlet convolution of one with this function returns the identity function. This function can be used to find the order of the ring Z over n Z, and a polygon is constructable if this function of the number of sides is equal to a power of two. For a prime input, this function returns one minus the input. This function appears 
Ford proved a result showing that for each k, the equation this function of x equals m has exactly k solutions. Jordan extended this function to k-tuples. This function appears in the denominator of the definition of the Silverman Constant. The Dirichlet convolution of one with this function returns the identity function. This function can be used to find the order of the ring Z over n Z, and a polygon is constructable if this function of the number of sides is equal to a power of two. For a prime input, this function returns one minus the input. This function appears in the exponent of its namesake's extension to Fermat's little theorem. For 10 points, name this function that returns the number of integers less than the input that are relatively prime to it.
Ford proved a result showing that for each k, the equation this function of x equals m has exactly k solutions.
Euler totient function [or Euler phi function]