query: The Möbius function is the sum of the primitive $n$th roots of unity.
positive_passages.docid: 26728
positive_passages.text: Coefficient of $n$th cyclotomic polynomial equals $-\mu(n)$
negative_passages.docid: 103552
negative_passages.text: The minimal polynomial of a primitive $p^{m}$-th root of unity over $\mathbb{Q}_p$
negative_passages.docid: 31633
negative_passages.text: Why is every holomorphic bijection of the Riemann sphere a Möbius transformation?
negative_passages.docid: 139305
negative_passages.text: Prove $f=1+x+x^2+x^3+\cdots+x^n$ has no multiple roots.
negative_passages.docid: 50823
negative_passages.text: Primitive polynomials
negative_passages.docid: 128575
negative_passages.text: Elementary proof that $3$ is a primitive root of a Fermat prime?
negative_passages.docid: 7500
negative_passages.text: $\arctan$ of a square root as a rational multiple of $\pi$
negative_passages.docid: 15202
negative_passages.text: the root of $N$th transpose matrix
negative_passages.docid: 122759
negative_passages.text: Show $2+\alpha$ is a primitive root of $\mathbb{F}_{25}$.
negative_passages.docid: 31076
negative_passages.text: Roots of unity filter, identity involving $\sum_{k \ge 0} \binom{n}{3k}$
negative_passages.docid: 44802
negative_passages.text: The $n$ complex $n$th roots of a complex number $z$
negative_passages.docid: 132126
negative_passages.text: Proving $\sum\limits_{n=1}^{\infty } \frac{\mu (n)}n=0$ where $\mu$ is the Möbius function
negative_passages.docid: 67271
negative_passages.text: $\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$
negative_passages.docid: 54358
negative_passages.text: Why $(1-\zeta)$ unit where $\zeta$ is a primitive nth and n divisible by two primes
negative_passages.docid: 41486
negative_passages.text: If $x^n + a_{n-1}x^{n-1} + ... + a_0 = 0$ has a rational root, then such root is an integer
negative_passages.docid: 106280
negative_passages.text: Integrating the formula for the sum of the first $n$ natural numbers
negative_passages.docid: 143069
negative_passages.text: What are the direct summands in $\mathbb{Z}^n$?