For 10 points, name this number-theoretic function giving the number of integers less than and coprime to its argument.
Gauss proved that an n-gon is constructible with compass and straightedge if and only if this function of n is a power of 2. This function of n gives the degree of the field extension when adjoining a primitive nth root of unity to Q. Taking the sum over this function applied to all (*) divisors of n returns n. As a corollary of the fact that the order of a subgroup divides the order of the finite group it's in, since this function of n gives the order of multiplicative group of integers mod n, any element of that group raised to this function of n equals 1, giving Euler's theorem. For any prime p, this function returns p-1. For 10 points, name this number-theoretic function giving the number of integers less than and coprime to its argument.
Gauss proved that an n-gon is constructible with compass and straightedge if and only if this function of n is a power of 2.
Euler's totient function [or Euler's phi function]