query: How to prove $\gcd(dm,dn)=d\cdot\gcd(m,n)$
positive_passages.docid: 7316
positive_passages.text: How to prove that $z\gcd(a,b)=\gcd(za,zb)$
negative_passages.docid: 80148
negative_passages.text: Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
negative_passages.docid: 23066
negative_passages.text: If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
negative_passages.docid: 2289
negative_passages.text: Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
negative_passages.docid: 156966
negative_passages.text: Prove that if $b = dk$ where $gcd(m, a) = d$, there are $d$ solutions to $ax \equiv b \mod m$
negative_passages.docid: 37808
negative_passages.text: Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
negative_passages.docid: 18772
negative_passages.text: If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
negative_passages.docid: 72747
negative_passages.text: Proving gcd($a,b$)lcm($a,b$) = $|ab|$
negative_passages.docid: 38404
negative_passages.text: Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
negative_passages.docid: 2208
negative_passages.text: $\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
negative_passages.docid: 32344
negative_passages.text: Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.
negative_passages.docid: 20003
negative_passages.text: Prove for positive integers a,b,c and d (where b does not equal d), if gcd(a,b) = gcd(c,d) = 1, then a/b + c/d is not an integer
negative_passages.docid: 102133
negative_passages.text: Prove: $\gcd(a,b) = \gcd(a, b + at)$.
negative_passages.docid: 34330
negative_passages.text: How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
negative_passages.docid: 147902
negative_passages.text: Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$
negative_passages.docid: 65218
negative_passages.text: Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
negative_passages.docid: 56612
negative_passages.text: Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]