query: If $A^n = B$ and I know $B$, can I find $A$?
positive_passages.docid: 109167
positive_passages.text: Nth roots of square matrices
negative_passages.docid: 63183
negative_passages.text: Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
negative_passages.docid: 106584
negative_passages.text: If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$
negative_passages.docid: 88995
negative_passages.text: Prove that $a^n-b^n = (a-b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})$.
negative_passages.docid: 82953
negative_passages.text: In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$
negative_passages.docid: 41792
negative_passages.text: If $abc=1$, then $\frac{a^{n+2}}{a^n+(n-1)b^n}+\frac{b^{n+2}}{b^n+(n-1)c^n}+\frac{c^{n+2}}{c^n+(n-1)a^n} \geq \frac{3}{n} $
negative_passages.docid: 104920
negative_passages.text: Can we find positive integers $a$ and $k \geq 2$ with $2^n - 1 = a^k$?
negative_passages.docid: 97411
negative_passages.text: If $x^n=y^n$ and $n$ is odd then $x=y$
negative_passages.docid: 98470
negative_passages.text: If $A \ne \varnothing$, then $\varnothing^A=\varnothing$
negative_passages.docid: 6096
negative_passages.text: If $A+B=AB$ then $AB=BA$
negative_passages.docid: 7817
negative_passages.text: Help to compute all powers $A^{n}$ and find is the matrix of $A$ diagonal?
negative_passages.docid: 80601
negative_passages.text: Let $a,b$ be in a group $G$. Show $(ab)^n=a^nb^n$ $\forall n\in\mathbb{Z}$ if and only if $ab=ba$.
negative_passages.docid: 127293
negative_passages.text: Prove that $(a-b) \mid (a^n-b^n)$
negative_passages.docid: 115866
negative_passages.text: Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
negative_passages.docid: 17176
negative_passages.text: Proof that $x^n \mod b = (x \mod b)^n$
negative_passages.docid: 24307
negative_passages.text: Is $x^x=y$ solvable for $x$?
negative_passages.docid: 21781
negative_passages.text: Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$