query: Proving $\gcd(ga, gb) = g\gcd(a, b)$ intuitively
positive_passages.docid: 6410
positive_passages.text: Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]
negative_passages.docid: 128820
negative_passages.text: Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
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: 154959
negative_passages.text: Proof of associativity of GCD?
negative_passages.docid: 24845
negative_passages.text: Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
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: 130112
negative_passages.text: If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
negative_passages.docid: 76507
negative_passages.text: $\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
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: 33996
negative_passages.text: Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
negative_passages.docid: 126358
negative_passages.text: Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
negative_passages.docid: 158025
negative_passages.text: Intuition of why $\gcd(a,b) = \gcd(b, a \pmod b)$?
negative_passages.docid: 36
negative_passages.text: Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
negative_passages.docid: 90480
negative_passages.text: Code for (a,b) with gcd(a,b)=1?
negative_passages.docid: 24160
negative_passages.text: Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
negative_passages.docid: 84501
negative_passages.text: Proof involving Cyclic group, generator and GCD
negative_passages.docid: 40848
negative_passages.text: $a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$