query: Is $d|b$ and $d|a$ true in $d = l \cdot a + k \cdot b$
positive_passages.docid: 28749
positive_passages.text: Proving that any common multiple of two numbers is a multiple of their least common multiple
negative_passages.docid: 55393
negative_passages.text: Existence of a group isomorphism between $(\mathbb K,+)$ and $(\mathbb K^\times,\cdot)$
negative_passages.docid: 41099
negative_passages.text: If $A \subseteq C$ and $B \subseteq D$ then $A \times B \subseteq C \times D$
negative_passages.docid: 112345
negative_passages.text: In an Integral Domain is it true that $\gcd(ac,ab) = a\gcd(c,b)$?
negative_passages.docid: 151607
negative_passages.text: Show that  $A\Delta B = C$ if and only if $A = B\Delta C$
negative_passages.docid: 6128
negative_passages.text: If $a \cdot a = 1$ then $a = 1$ or $a = -1$
negative_passages.docid: 111665
negative_passages.text: How prove this $\{a\}\cdot\{b\}\cdot\{c\}=0$ if $\lfloor na\rfloor+\lfloor nb\rfloor=\lfloor nc\rfloor$
negative_passages.docid: 55441
negative_passages.text: Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
negative_passages.docid: 117922
negative_passages.text: Is $\frac{a+b}{c+d}0$?
negative_passages.docid: 41558
negative_passages.text: Prove that $\frac4{abcd} \geq \frac a b + \frac bc + \frac cd +\frac d a$
negative_passages.docid: 7151
negative_passages.text: Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.
negative_passages.docid: 24912
negative_passages.text: Show that if $fd'=f'd $ and the pairs $f, d $ and $f',d' $ are coprime, then $f=f' $ and $d=d' $.
negative_passages.docid: 61666
negative_passages.text: Proving $ [(\vec{a}+\vec{b})\times(\vec{b}+\vec{c})]\cdot(\vec{c}+\vec{a})=2\vec{c}\cdot(\vec{b}\times\vec{a})$
negative_passages.docid: 19656
negative_passages.text: Proving that $ \gcd(a,b) = as + bt $, i.e., $ \gcd $ is a linear combination.
negative_passages.docid: 147527
negative_passages.text: Let $a$ and $b$ be non-zero integers, and $c$ be an integer. Let $d = \gcd(a, b)$. Prove that if $a|c$ and $b|c$ then $ab|cd$.
negative_passages.docid: 62342
negative_passages.text: $x_1 \cdot \dots \cdot x_n=1 \implies x_1 + \dots + x_n \ge n$
negative_passages.docid: 76049
negative_passages.text: Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$