query: How to show that any two equivalence classes of non-zero elements in $\mathbb{Z}_{p}$ have the same number of elements
positive_passages.docid: 158106
positive_passages.text: Prove that 1 less than the number of equivalence classes divides $p-1$ where $p$ is prime
negative_passages.docid: 59459
negative_passages.text: Binary sequences and ${2}^{\mathbb{N}}$ have the same cardinality
negative_passages.docid: 84132
negative_passages.text: Number of preimages of a group element under a homomorphism.
negative_passages.docid: 108044
negative_passages.text: Isomorphic extensions of $\mathbb Z_3$ by $\mathbb Z_3 \times \mathbb Z_3$ which are not equivalent
negative_passages.docid: 117862
negative_passages.text: Number of partitions of an $n$-element set into $k$ classes
negative_passages.docid: 21250
negative_passages.text: Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
negative_passages.docid: 63129
negative_passages.text: Infinite number of $k$ satisfying $p_{k+1} - p_{k} > 2$?
negative_passages.docid: 115973
negative_passages.text: Computing the number of nonisomorphic finite abelian groups of order $n$
negative_passages.docid: 89415
negative_passages.text: Number of homomorphisms from $(\mathbb Q^+ , \,\cdot\,)$ to $(\mathbb Z_n , +)$
negative_passages.docid: 128300
negative_passages.text: Prove that a group with exactly two proper nontrivial subgroups is isomorphic to $\mathbb{Z}_{pq}$ or $\mathbb{Z}_{p^3}$.
negative_passages.docid: 92583
negative_passages.text: Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
negative_passages.docid: 64527
negative_passages.text: Show that an operation of elements in a finite group contains each element exactly once
negative_passages.docid: 15387
negative_passages.text: Order of $GL(n, \mathbb Z_p)$
negative_passages.docid: 145752
negative_passages.text: Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
negative_passages.docid: 35362
negative_passages.text: Number of equivalence relations on a set
negative_passages.docid: 90433
negative_passages.text: Isomorphisms between $(\mathbb Z_4,+)$ and $(U_5,*)$
negative_passages.docid: 124333
negative_passages.text: A bijection between $\mathbb{N}$ and $\mathbb{P}(\mathbb{N})$?