query: Prove that every non-zero element of $\Bbb Z_p$ has an order which divides $p-1$.
positive_passages.docid: 17316
positive_passages.text: If $a^\phi = 1$ then the order of $a$ divides $\phi$
negative_passages.docid: 77209
negative_passages.text: Reducibility of $x^3+nx+1$ over $ \Bbb Z$
negative_passages.docid: 80144
negative_passages.text: Prove that $x-1$ divides $x^n-1$
negative_passages.docid: 101345
negative_passages.text: Suppose $n$ is an even positive integer and $H$ is a subgroup of $\mathbb Z/n \mathbb Z$. Prove that either every element of $H$ is...
negative_passages.docid: 7899
negative_passages.text: Show that if $p$ is prime then $\Bbb Z_p$ is a field
negative_passages.docid: 97833
negative_passages.text: Prove that if $k\mid m,$ then $Z_m$ has a subgroup of order $k.$
negative_passages.docid: 145406
negative_passages.text: Prove every element of $G$ has finite order.
negative_passages.docid: 122125
negative_passages.text: Order of group element divides order of finite group
negative_passages.docid: 119180
negative_passages.text: How to prove that the set $A = \left\{ {p:{p^2} < 2,p \in {\Bbb Q^+}} \right\}$ has no greatest element?
negative_passages.docid: 134676
negative_passages.text: Number of elements of order $p$ is a multiple of $p-1$ (finite group).
negative_passages.docid: 96062
negative_passages.text: Show $\underbrace{{111\cdots}1}_{{\small{p-1} \ 1's}}$ is divisible by $p$
negative_passages.docid: 110876
negative_passages.text: Prove that $p\mid \binom{p}{k},\ 0< k< p$
negative_passages.docid: 131946
negative_passages.text: Order of an Element Under a Homomorphism
negative_passages.docid: 119808
negative_passages.text: Proving that $n$-cycle has order $n$
negative_passages.docid: 29802
negative_passages.text: Part of simple proof of nontrivial center in p-group
negative_passages.docid: 66169
negative_passages.text: Ring of order $n$ is isomorphic to $\Bbb Z/n\Bbb Z$, with $n$ square-free
negative_passages.docid: 77076
negative_passages.text: Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$