MathDB
S 38

Source:

May 25, 2007
functiontrigonometrycalculusintegrationMiscellaneous Problems

Problem Statement

The function μ:N→C\mu: \mathbb{N}\to \mathbb{C} is defined by μ(n)=∑k∈Rn(cos⁡2kπn+isin⁡2kπn),\mu(n) = \sum^{}_{k \in R_{n}}\left( \cos \frac{2k\pi}{n}+i \sin \frac{2k\pi}{n}\right), where Rn={k∈N∣1≤k≤n,gcd⁡(k,n)=1}R_{n}=\{ k \in \mathbb{N}\vert 1 \le k \le n, \gcd(k, n)=1 \}. Show that μ(n)\mu(n) is an integer for all positive integer nn.
Back to ProblemsView on AoPS