query: If c = gcd(a, b), prove that gcd( a/c , b/c ) = 1
positive_passages.docid: 135086
positive_passages.text: GCD of two numbers divided by their greatest common divisor is 1
negative_passages.docid: 147802
negative_passages.text: Proving that $\gcd\left(\frac a {\gcd(a,b)},\frac b {\gcd(a,b)}\right) =1$
negative_passages.docid: 157508
negative_passages.text: prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
negative_passages.docid: 55673
negative_passages.text: Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?
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: 91506
negative_passages.text: If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
negative_passages.docid: 37808
negative_passages.text: Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
negative_passages.docid: 107914
negative_passages.text: Expanding GCDs Reasoning: $\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$
negative_passages.docid: 72424
negative_passages.text: Suppose 1 ≤ k ≤ n − 1 and gcd(k, n) = 1. Prove that gcd(n − k, n) = 1
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: 60842
negative_passages.text: if $a^2+b^2=c^2$ then $gcd(a,b)=gcd(a,c)=gcd(b,c)$.
negative_passages.docid: 118809
negative_passages.text: If $a$ divides $bc$ and $\gcd(a,b) = d$ then $\frac a d$ divides c
negative_passages.docid: 59006
negative_passages.text: Proof of $\gcd(n!+1, (n+1)!+1)=1$?
negative_passages.docid: 5708
negative_passages.text: Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
negative_passages.docid: 105832
negative_passages.text: prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
negative_passages.docid: 28021
negative_passages.text: Showing that these two definitions of $\gcd(a,b)$ are equivalent
negative_passages.docid: 142693
negative_passages.text: $\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$