query: Show that there exists $\alpha,\beta\in\mathbb{Z}^*_{n}$
positive_passages.docid: 149661
positive_passages.text: For $n=pq$, show that there exist $\alpha, \beta \in Z_n^*$ such that $\alpha, \beta \notin (Z_n^*)^2$ and $\alpha \cdot \beta \notin (Z_n^*)^2$.
negative_passages.docid: 72144
negative_passages.text: Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
negative_passages.docid: 83001
negative_passages.text: Easier way to show $(\mathbb{Z}/(n))[x]$ and $\mathbb{Z}[x] / (n)$ are isomorphic
negative_passages.docid: 142168
negative_passages.text: can we a prove ⊢ (α → α) → (α → α)
negative_passages.docid: 143067
negative_passages.text: Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.
negative_passages.docid: 125164
negative_passages.text: How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
negative_passages.docid: 142631
negative_passages.text: Show that A has the same cardinality as $A\setminus\{x,y,z\}$
negative_passages.docid: 10236
negative_passages.text: Show that $a^n \mid b^n$ implies $a \mid b$
negative_passages.docid: 110662
negative_passages.text: Show that $P(\mathbb{N})$ is equivalent to $2^\mathbb{N}$
negative_passages.docid: 143069
negative_passages.text: What are the direct summands in $\mathbb{Z}^n$?
negative_passages.docid: 75373
negative_passages.text: Show that $2^n>n$ for $n\in \mathbb{N}$
negative_passages.docid: 46831
negative_passages.text: Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
negative_passages.docid: 120010
negative_passages.text: Show that $\aleph_{\alpha}^{\aleph_{1}} = \aleph_{\alpha}^{\aleph_{0}}\cdot 2^{\aleph_1}$
negative_passages.docid: 12210
negative_passages.text: Show that $a^{61} \equiv a\pmod{1001}$ for every $a \in \mathbb{N}$
negative_passages.docid: 122932
negative_passages.text: When $(\mathbb{Q}(\zeta_n) : \mathbb{Q}) = 2$?
negative_passages.docid: 148585
negative_passages.text: Show that, for any $\epsilon>0$, there exist two rationals such that $q < x < q'$ and $|q-q'|<\epsilon$
negative_passages.docid: 133528
negative_passages.text: $\lvert K(\alpha_1,\dots,\alpha_n) : K \rvert$ is a divisor of $n!$