query: Suppose that $a, m$ and $n$ are positive integers such that $(m, n)=1$. If $m\mid a$ and $n\mid a$, then $mn\mid a$.
positive_passages.docid: 1991
positive_passages.text: If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$
negative_passages.docid: 134365
negative_passages.text: When is this true: If $m^2$ is a multiple of N then m is a multiple of N
negative_passages.docid: 108504
negative_passages.text: Prove that for all non-negative integers $m,n$, $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is an integer.
negative_passages.docid: 155545
negative_passages.text: Showing that $a \mid b$ and $b \mid a$ if and only if $a= \pm b$.
negative_passages.docid: 88662
negative_passages.text: $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer.
negative_passages.docid: 13026
negative_passages.text: Prove that if AB=I_m, then rk(A)=rk(B).
negative_passages.docid: 106416
negative_passages.text: If $n,m \in \mathbb{N}$ then there are $c,d$ such that $cd = (m,n)$, $(c,d) = 1$ and $(m/c,n/d) = 1$.
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: 25784
negative_passages.text: Let $x$ and $y$ be positive integers such that $xy \mid x^2+y^2+1$.
negative_passages.docid: 17677
negative_passages.text: Prove or show a counter example for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$
negative_passages.docid: 147902
negative_passages.text: Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$
negative_passages.docid: 28796
negative_passages.text: Use the Inclusion-Exclusion Principle to show that for any non-negative integers $m, r, n$ such that $m≤r≤n$...
negative_passages.docid: 153670
negative_passages.text: Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
negative_passages.docid: 31331
negative_passages.text: $|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
negative_passages.docid: 11127
negative_passages.text: Let $a$, $b$, and $c$ be positive real numbers.
negative_passages.docid: 75199
negative_passages.text: $a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
negative_passages.docid: 21006
negative_passages.text: Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$?