Suppose that $p$ is a prime. Prove that the sum of the primitive roots modulo $p$ is congruent to $\mu(p − 1) \pmod{p}$.
Prove sum of primitive roots congruent to $\mu(p-1) \pmod{p}$
13
$\begingroup$
number-theory
primitive-roots
mobius-function
-
11Please don't post questions in the imperative mode; this may be homework for you, but you aren't assigning it as homework to *us*. You are asking a question, so kindly phrase it like a question. Also, given that this is homework, it would be nice (and polite, and helpful) if you say what you have tried, and where you are stuck. That way the answers can deal directly with whatever it is you are having trouble with. – 2011-03-07
-
4Hint: If $latex f = x^n + f_{n-1} x^{n-1} + \cdots + f_0$ is a polynomial whose roots are $r_1$, ..., $r_n$, then $- \sum r_i = f_{n-1}$. – 2011-03-07
-
0I've seen this result in a few books. But I can't see why it is interesting. Can someone please enlighten me? – 2012-01-12
-
0Related: http://math.stackexchange.com/questions/737892 – 2015-03-14