query: If $n^n|m^m$, is it true that $n|m$?
positive_passages.docid: 14581
positive_passages.text: How do we prove $n^n \mid m^m \Rightarrow n \mid m$?
negative_passages.docid: 100305
negative_passages.text: Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
negative_passages.docid: 25419
negative_passages.text: If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$
negative_passages.docid: 28136
negative_passages.text: $A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$
negative_passages.docid: 134739
negative_passages.text: product of divisors of n as a power of n.
negative_passages.docid: 43246
negative_passages.text: Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
negative_passages.docid: 33866
negative_passages.text: Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
negative_passages.docid: 158082
negative_passages.text: Is $\|A^n\|=\|A\|^n$ true for any normal operator in a Hilbert space?
negative_passages.docid: 31331
negative_passages.text: $|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
negative_passages.docid: 39453
negative_passages.text: How do I prove that $S^n$ is homeomorphic to $S^m \Rightarrow m=n$?
negative_passages.docid: 24403
negative_passages.text: Prove that $ n < 2^{n}$ for all natural numbers $n$.
negative_passages.docid: 79056
negative_passages.text: Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
negative_passages.docid: 62474
negative_passages.text: If $AB=I_n$ and $BA=I_m$ then $n=m$.
negative_passages.docid: 55273
negative_passages.text: Prove by mathematical induction that: $\forall n \in \mathbb{N}: 3^{n} > n^{3}$
negative_passages.docid: 150958
negative_passages.text: Group theory question. If $m$ and $n$ are relatively prime, and $a$, $b$ belong to group and $a^m = b^m$ and $a^n = b^n$, how would one prove $a = b$?
negative_passages.docid: 124685
negative_passages.text: How to show $(mn)!$ is divisible by $(m!)^n$?
negative_passages.docid: 38549
negative_passages.text: $\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$