query: Let $n$ be positive and $a > 1$. Show that $\gcd(\frac{a^n - 1}{a-1}, a-1) = \gcd(a-1, n)$
positive_passages.docid: 23590
positive_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: 77064
negative_passages.text: Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
negative_passages.docid: 66748
negative_passages.text: Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
negative_passages.docid: 27544
negative_passages.text: With $a,\ b,\ m,\ n\in \mathbb{Z}$. Show that if ${\rm gcd}(m,n)=1$, then ${\rm gcd}(ma+nb,mn)={\rm gcd}(a,n){\rm gcd}(b,m)$
negative_passages.docid: 1991
negative_passages.text: If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$
negative_passages.docid: 32108
negative_passages.text: $ a\in \Bbb Z_n$ is invertible $\,\Rightarrow\gcd (a,n) =1$
negative_passages.docid: 91506
negative_passages.text: If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
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: 19046
negative_passages.text: Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n
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: 59006
negative_passages.text: Proof of $\gcd(n!+1, (n+1)!+1)=1$?
negative_passages.docid: 86413
negative_passages.text: Show that $\frac{(m+n-1)!}{m!n!}$ is an integer where m and n are positive integers and gcd(m,n)=1
negative_passages.docid: 88662
negative_passages.text: $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer.
negative_passages.docid: 83307
negative_passages.text: If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
negative_passages.docid: 8160
negative_passages.text: What is $\gcd(0,a)$, where $a$ is a positive integer?
negative_passages.docid: 102133
negative_passages.text: Prove: $\gcd(a,b) = \gcd(a, b + at)$.
negative_passages.docid: 19700
negative_passages.text: Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$