query: Can you factor out a common divisor when finding $\gcd(a,b)$?
positive_passages.docid: 149993
positive_passages.text: Use the Euclidean algorithm to prove that gcd(na, nb) = n gcd(a, b).
negative_passages.docid: 65687
negative_passages.text: $\gcd(a,b)\gcd(x,y)\mid ax+by$
negative_passages.docid: 23066
negative_passages.text: If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
negative_passages.docid: 66748
negative_passages.text: Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
negative_passages.docid: 62959
negative_passages.text: How to find GCD, LCM on a set of numbers
negative_passages.docid: 14693
negative_passages.text: $d = \gcd(c,m),\ ac≡bc\pmod{\! m}\Rightarrow a≡b\pmod {\!m/d}\ $ [Congruence Cancellation & Division Rule]
negative_passages.docid: 142693
negative_passages.text: $\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
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: 25573
negative_passages.text: If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
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: 101940
negative_passages.text: If we know the GCD and LCM of two integers, can we determine the possible values of these two integers?
negative_passages.docid: 66785
negative_passages.text: Find $\gcd(p^n-1,p^m+1)$.
negative_passages.docid: 65503
negative_passages.text: Identity involving LCM and GCD: $\frac{[a,b,c]^2}{[a,b][b,c][c,a]}=\frac{(a,b,c)^2}{(a,b)(b,c)(c,a)}$
negative_passages.docid: 91506
negative_passages.text: If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
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: 122096
negative_passages.text: Find $GCD(n^2+1,n+1)$
negative_passages.docid: 19500
negative_passages.text: How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?