query: How many elements generate the cyclic group $\mathbb{Z}/p^r\mathbb{Z}$?
positive_passages.docid: 106653
positive_passages.text: How many generator has a cyclic group of order n?
negative_passages.docid: 68201
negative_passages.text: Cyclic group of order $n$
negative_passages.docid: 58397
negative_passages.text: Every cyclic group with order > 2 has at least 2 distinct generators
negative_passages.docid: 20097
negative_passages.text: Cardinality of the quotient ring $\mathbb{Z}[x]/(x^2-3,2x+4)$
negative_passages.docid: 22084
negative_passages.text: $\mathbb{Z}[i] / (2+3i)$ has 13 elements
negative_passages.docid: 108775
negative_passages.text: Identify the ring $\mathbb {Z}[i]/(2 + i) $
negative_passages.docid: 127306
negative_passages.text: Is the group of units of a finite ring cyclic?
negative_passages.docid: 144789
negative_passages.text: identify the ring $\mathbb{Z}[x]/(2x-1)$
negative_passages.docid: 134872
negative_passages.text: Generators of $\text{GL}_{2}(\mathbb{Z})$ group, good reference book?
negative_passages.docid: 47522
negative_passages.text: group generators of $(\mathbb Z_{17}-\{0\},\times)$
negative_passages.docid: 5699
negative_passages.text: The number of ring homomorphisms from $\mathbb{Z}_m$ to $\mathbb{Z}_n$
negative_passages.docid: 158074
negative_passages.text: Cyclic group $G$ with generator $ab$.
negative_passages.docid: 128899
negative_passages.text: How to find all generators for a cyclic group of order $n$?
negative_passages.docid: 132725
negative_passages.text: Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$?
negative_passages.docid: 124438
negative_passages.text: Find $|(\mathbb{Z} \oplus \mathbb{Z}) / \langle(3,6)\rangle|$ and determine if its cyclic
negative_passages.docid: 27704
negative_passages.text: Cardinality of quotient ring $\mathbb{Z_6}[X]/(2X+4)$
negative_passages.docid: 45947
negative_passages.text: Find generator of multiplicative group of $\mathbb{F}_{27}$