query: Find the number of generators of a cyclic group with a given order n
positive_passages.docid: 53357
positive_passages.text: Cyclic Group Generators of Order $n$
negative_passages.docid: 13734
negative_passages.text: Show that every group of prime order is cyclic
negative_passages.docid: 41231
negative_passages.text: Subgroups of (Z,+) of order n
negative_passages.docid: 152653
negative_passages.text: Count Eulerian cycles in $K_{n,2}$
negative_passages.docid: 39938
negative_passages.text: Subgroups of a cyclic group and their order.
negative_passages.docid: 3829
negative_passages.text: Number of automorphisms of a direct product of two cyclic $p$-groups
negative_passages.docid: 84132
negative_passages.text: Number of preimages of a group element under a homomorphism.
negative_passages.docid: 142477
negative_passages.text: Closed-form expression for the number of $k$-permutations of length $n$. Duplicates allowed!
negative_passages.docid: 68971
negative_passages.text: Elementary approach to proving that a group of order 9 is Abelian
negative_passages.docid: 58397
negative_passages.text: Every cyclic group with order > 2 has at least 2 distinct generators
negative_passages.docid: 147517
negative_passages.text: Any group of order $n$ satisfying $\gcd (n, \varphi(n)) =1$ is cyclic
negative_passages.docid: 14890
negative_passages.text: Let $G=\langle a\rangle$ be a cyclic group of order $n$. Show that, for every divisor $d$ of $n$, there exists a subgroup of $G$ whose order is $d$.
negative_passages.docid: 15000
negative_passages.text: Show that number of elements in $(Z/nZ)^*$ is $\phi (n)$
negative_passages.docid: 25744
negative_passages.text: Multiplication in Permutation Groups Written in Cyclic Notation
negative_passages.docid: 84501
negative_passages.text: Proof involving Cyclic group, generator and GCD
negative_passages.docid: 62035
negative_passages.text: Order of automorphism group of cyclic group
negative_passages.docid: 142038
negative_passages.text: Finding the number of elements of order two in the symmetric group $S_4$