query: $a|b \land b|a \iff a = \pm b$
positive_passages.docid: 155545
positive_passages.text: Showing that $a \mid b$ and $b \mid a$ if and only if $a= \pm b$.
negative_passages.docid: 111763
negative_passages.text: True or False $A - C = B - C $ if and only if $A \cup C = B \cup C$
negative_passages.docid: 100426
negative_passages.text: Let $a$ and $b$ be integers. Show that if $a \equiv b \pmod{p}$ for every prime $p$, then $a = b$.
negative_passages.docid: 63535
negative_passages.text: Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
negative_passages.docid: 15626
negative_passages.text: Relations of a~b iff b = ak^2
negative_passages.docid: 56399
negative_passages.text: Proof for $A \cup B = B$ if and only if $A \subset B$
negative_passages.docid: 113735
negative_passages.text: Do we need to prove that if x∉A in proposition "if A⊆B then A⋃B=B"?
negative_passages.docid: 834
negative_passages.text: If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.
negative_passages.docid: 118981
negative_passages.text: Proving $\sqrt{ab} = \sqrt a\sqrt b$
negative_passages.docid: 119156
negative_passages.text: $(a,b)=d \overset{?}{\implies} (a^3,b^3)=d^3$
negative_passages.docid: 63267
negative_passages.text: Under what conditions on the sets $A$ and $B$ will it be true that $A\times B= B\times A$
negative_passages.docid: 31465
negative_passages.text: Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
negative_passages.docid: 30583
negative_passages.text: If $a\mid b$ and $b\mid a$, $a,b\in R$, show that $\exists w \in R^\times$ with $b=wa$
negative_passages.docid: 152693
negative_passages.text: If $C|a$ and $C|b$ then $C|(ax+by)$
negative_passages.docid: 87327
negative_passages.text: Unions and intersections: $(A \cup B = A ∪ C) \land (A \cap B = A ∩ C) \implies B = C.$
negative_passages.docid: 83475
negative_passages.text: Prove Or Disprove: tr(AB)=tr(A)*tr(B)
negative_passages.docid: 3301
negative_passages.text: If $AB = I$ then $BA = I$