For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
27544
With $a,\ b,\ m,\ n\in \mathbb{Z}$. Show that if ${\rm gcd}(m,n)=1$, then ${\rm gcd}(ma+nb,mn)={\rm gcd}(a,n){\rm gcd}(b,m)$
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
23590
Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
67660
Prove $\,b\equiv c\pmod{\!m}\Rightarrow \gcd(b,m)=\gcd(c,m)$ i.e. $\gcd(c+km,m) = \gcd(c,m)$
107914
Expanding GCDs Reasoning: $\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$