query: If $(b,c) = 1$, then $(a,bc) = (a,b)(a,c)$
positive_passages.docid: 21726
positive_passages.text: Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
negative_passages.docid: 13012
negative_passages.text: Why can a = b imply 2 = 1?
negative_passages.docid: 33542
negative_passages.text: When is $A- B = B- A$?
negative_passages.docid: 53660
negative_passages.text: Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
negative_passages.docid: 10348
negative_passages.text: Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
negative_passages.docid: 62474
negative_passages.text: If $AB=I_n$ and $BA=I_m$ then $n=m$.
negative_passages.docid: 153670
negative_passages.text: Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
negative_passages.docid: 3301
negative_passages.text: If $AB = I$ then $BA = I$
negative_passages.docid: 76823
negative_passages.text: Is it the case that for all sets $A, B, C,$ and $D$, $(A \times B) \cup (C \times D) = (A \cup B) \times (C \cup D)$?
negative_passages.docid: 40848
negative_passages.text: $a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
negative_passages.docid: 43219
negative_passages.text: If $[K(\alpha):K]=p\neq q=[K(\beta):K]$ then $[K(\alpha+\beta):K]=pq$
negative_passages.docid: 24845
negative_passages.text: Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
negative_passages.docid: 51321
negative_passages.text: Prove that $A = B = C = D$
negative_passages.docid: 139018
negative_passages.text: A does the same B as does C
negative_passages.docid: 1991
negative_passages.text: If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$
negative_passages.docid: 111003
negative_passages.text: Prove that if $A\triangle B = C\triangle B$, then $A = C$
negative_passages.docid: 135779
negative_passages.text: Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.