query: Prove: if $d=\text{gcd}(m,n)$ so $\text{gcd}\left(\frac{m}{d},\frac{n}{d}\right)=1$
positive_passages.docid: 49109
positive_passages.text: Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
negative_passages.docid: 18714
negative_passages.text: $\gcd\left(a+b,\frac{a^p+b^p}{a+b}\right)=1$, or $p$
negative_passages.docid: 48452
negative_passages.text: Proof that $\gcd$ divides $\operatorname{lcm}$
negative_passages.docid: 106416
negative_passages.text: If $n,m \in \mathbb{N}$ then there are $c,d$ such that $cd = (m,n)$, $(c,d) = 1$ and $(m/c,n/d) = 1$.
negative_passages.docid: 7090
negative_passages.text: Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$
negative_passages.docid: 51858
negative_passages.text: Showing $\gcd(2^m-1,2^n+1)=1$
negative_passages.docid: 69967
negative_passages.text: How to prove $\gcd(a^m-b^m,a^n-b^n) = a^{\gcd(m,n)} - b^{\gcd(m,n)} $?
negative_passages.docid: 6012
negative_passages.text: Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
negative_passages.docid: 154959
negative_passages.text: Proof of associativity of GCD?
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: 10348
negative_passages.text: Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
negative_passages.docid: 95889
negative_passages.text: Prove that $\gcd(n! + 1, 3n! + 1) = 1$, $\forall n \in \mathbb{N}$, $n \geq 2$.
negative_passages.docid: 110313
negative_passages.text: Prove that $\gcd(f(x),g(x)) = 1$.
negative_passages.docid: 33996
negative_passages.text: Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
negative_passages.docid: 74924
negative_passages.text: identity element of $(D_n ,\gcd)$
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: 7316
negative_passages.text: How to prove that $z\gcd(a,b)=\gcd(za,zb)$