query: Number of solutions to $x^n=e$ in group G is divisible by n, where n divides o(G)
positive_passages.docid: 147596
positive_passages.text: Number of solutions to $x^n=e$ in group $G$ is divisible by $n$
negative_passages.docid: 101602
negative_passages.text: consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
negative_passages.docid: 11003
negative_passages.text: Proving that $G/N$ is an abelian group
negative_passages.docid: 154610
negative_passages.text: Number of solutions for the given equation in finite field of order 32.
negative_passages.docid: 100605
negative_passages.text: let $G$ to be finite abelian group of order O(G), let n to be prime number and (O(G),n)=1 prove that $g=x^n$ for any $ x \in G$
negative_passages.docid: 94407
negative_passages.text: Number of solutions for $x[1] + x[2] + \ldots + x[n] =k$
negative_passages.docid: 40131
negative_passages.text: If n is such that every element $(\mathbb{Z}/n\mathbb{Z})^{\times}$ is a root of $x^2-1$. Prove that $n$ divides 24.
negative_passages.docid: 1001
negative_passages.text: Number of integer solutions of $x^2 + y^2 = k$
negative_passages.docid: 82571
negative_passages.text: Number of solutions of $x^2=1$ in $\mathbb{Z}/n\mathbb{Z}$
negative_passages.docid: 79940
negative_passages.text: $\binom{p}{i}$ divisible by $p$, with $p$ prime
negative_passages.docid: 53357
negative_passages.text: Cyclic Group Generators of Order $n$
negative_passages.docid: 152604
negative_passages.text: For a finite group of order $2n$ does there exist $x$ such that $x\ast x=e$?
negative_passages.docid: 117761
negative_passages.text: When is $\binom{n}{k}$ divisible by $n$?
negative_passages.docid: 104965
negative_passages.text: Find $n$ such that polynomial is divisible
negative_passages.docid: 5297
negative_passages.text: If G is a finite abelian group and $a_1,...,a_n$ are all its elements, show that $x=a_1a_2a_3...a_n$must satisfy $x^2=e$.
negative_passages.docid: 104549
negative_passages.text: When $d \mid n$, the number of elements of order $d$ in a cyclic subgroup of order $n$ is $\phi (d)$
negative_passages.docid: 56650
negative_passages.text: Prove that $(G, \circ)$ is a group if $a\circ x = b$ and $x\circ a = b$ have unique solutions