How to prove $\gcd(a-bc, b) =\gcd(a,b)$ for $a,b,c \in \mathbb{Z}$?
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
82777
If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$?
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
125737
GCD( LCM(a,b) , LCM(a,c) ) = LCM(b, GCD(b,c)) , why?
25825
Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
149993
Use the Euclidean algorithm to prove that gcd(na, nb) = n gcd(a, b).
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
147527
Let $a$ and $b$ be non-zero integers, and $c$ be an integer. Let $d = \gcd(a, b)$. Prove that if $a|c$ and $b|c$ then $ab|cd$.
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
73972
How to prove that $\gcd(2n^3-14n+2,n+3) = \gcd(n+3,10)$?
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $