query: Is it true that $\gcd(ta,tb)=t\gcd(a,b)$ in a domain?
positive_passages.docid: 19822
positive_passages.text: For $D$ a GCD domain , let $a,b,x \in D \setminus \{0\}$ , then is it true that $\gcd (ax,bx)=x \cdot \gcd (a,b)$?
negative_passages.docid: 57281
negative_passages.text: Is Bezout's lemma enough to confirm the GCD of a number.
negative_passages.docid: 76680
negative_passages.text: Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
negative_passages.docid: 2208
negative_passages.text: $\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
negative_passages.docid: 157784
negative_passages.text: Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
negative_passages.docid: 34330
negative_passages.text: How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
negative_passages.docid: 23590
negative_passages.text: Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$
negative_passages.docid: 37596
negative_passages.text: If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
negative_passages.docid: 78678
negative_passages.text: If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
negative_passages.docid: 74924
negative_passages.text: identity element of $(D_n ,\gcd)$
negative_passages.docid: 130112
negative_passages.text: If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
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: 19164
negative_passages.text: On the GCD of a Pair of Fermat Numbers
negative_passages.docid: 60842
negative_passages.text: if $a^2+b^2=c^2$ then $gcd(a,b)=gcd(a,c)=gcd(b,c)$.
negative_passages.docid: 38404
negative_passages.text: Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
negative_passages.docid: 154959
negative_passages.text: Proof of associativity of GCD?
negative_passages.docid: 91506
negative_passages.text: If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$