query: Show that $x^n -1 \mid x^k -1 \Leftrightarrow n \mid k$
positive_passages.docid: 27281
positive_passages.text: How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
negative_passages.docid: 39563
negative_passages.text: How to show $a,b$ coprime to $n\Rightarrow ab$ coprime to $n$?
negative_passages.docid: 55266
negative_passages.text: Prove that $(n+1)^{n-1}<n^n$
negative_passages.docid: 7491
negative_passages.text: How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?
negative_passages.docid: 34017
negative_passages.text: Show that $n^{\pi\left(2n\right)-\pi\left(n\right)}2$
negative_passages.docid: 45742
negative_passages.text: Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
negative_passages.docid: 90283
negative_passages.text: Proof that $3 \mid \left( a^2+b^2 \right)$ iff $3 \mid \gcd \left( a,b\right)$
negative_passages.docid: 146093
negative_passages.text: Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
negative_passages.docid: 143543
negative_passages.text: Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
negative_passages.docid: 75373
negative_passages.text: Show that $2^n>n$ for $n\in \mathbb{N}$
negative_passages.docid: 19701
negative_passages.text: Prove $5\mid2^{4n}-1$ by induction
negative_passages.docid: 136274
negative_passages.text: $n! \leq \left( \frac{n+1}{2} \right)^n$ via induction
negative_passages.docid: 123275
negative_passages.text: Prove $[A,B^n] = nB^{n-1}[A,B]$
negative_passages.docid: 106767
negative_passages.text: $|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
negative_passages.docid: 4970
negative_passages.text: For $n \geq 2$, show that $n \nmid 2^{n}-1$
negative_passages.docid: 136077
negative_passages.text: Prove that $x-1$ is a factor of $x^n-1$
negative_passages.docid: 136304
negative_passages.text: Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$