query: Show that for a and b non-zero integers and c different from zero, then gcd(ca,bc) = |c|gcd(a,b)
positive_passages.docid: 7316
positive_passages.text: How to prove that $z\gcd(a,b)=\gcd(za,zb)$
negative_passages.docid: 19700
negative_passages.text: Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$
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: 28021
negative_passages.text: Showing that these two definitions of $\gcd(a,b)$ are equivalent
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: 37808
negative_passages.text: Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
negative_passages.docid: 66748
negative_passages.text: Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
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: 121156
negative_passages.text: Prove that: $\gcd[a,b,c]=\frac{abc.\operatorname{lcm}(a,b,c)}{\operatorname{lcm}(a,b)\operatorname{lcm}(a,c)\operatorname{lcm}(b,c)}$
negative_passages.docid: 44076
negative_passages.text: Proving if $d_0$ is the smallest positive integer in $S$ then $d_0 = \gcd(a,b)$
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: 87013
negative_passages.text: If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
negative_passages.docid: 25573
negative_passages.text: If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
negative_passages.docid: 49109
negative_passages.text: Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
negative_passages.docid: 2289
negative_passages.text: Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
negative_passages.docid: 25907
negative_passages.text: Show $a\Bbb Z+b\Bbb Z = \gcd(a,b)\Bbb Z$
negative_passages.docid: 84417
negative_passages.text: Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$