query: If a|b and b|c , (how can I prove) ⇒ a|c?
positive_passages.docid: 153670
positive_passages.text: Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
negative_passages.docid: 31465
negative_passages.text: Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
negative_passages.docid: 22856
negative_passages.text: Ways to go from A to B(proof)
negative_passages.docid: 48484
negative_passages.text: Prove that $6|a+b+c$ if and only if $6|a^3+b^3+c^3$
negative_passages.docid: 144693
negative_passages.text: Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
negative_passages.docid: 65280
negative_passages.text: If $a, b, c >0$ prove that $ [(1+a)(1+b)(1+c)]^7 > 7^7a^4b^4c^4 $.
negative_passages.docid: 84946
negative_passages.text: If $0<a<b$, prove that $a<\sqrt{ab}<\frac{a+b}{2}<b$
negative_passages.docid: 111003
negative_passages.text: Prove that if $A\triangle B = C\triangle B$, then $A = C$
negative_passages.docid: 21726
negative_passages.text: Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
negative_passages.docid: 26766
negative_passages.text: Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
negative_passages.docid: 109778
negative_passages.text: Proving $(x-c)|(p(x)-p(c))$
negative_passages.docid: 31196
negative_passages.text: Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$
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: 141102
negative_passages.text: If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.
negative_passages.docid: 64586
negative_passages.text: How to prove that $\neg((A\cap B)\cup (\neg A \cap C)) = (A\cap\neg B)\cup (\neg A\cap \neg C)$
negative_passages.docid: 97667
negative_passages.text: If $a<b$, $c<d$ then $a+c<b+d$?
negative_passages.docid: 135779
negative_passages.text: Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.