Let $n$ and $k$ be positive integers. Show that $\gcd(n, nk + 1) = 1$
190
Why $\gcd(qb+r,b)=\gcd(b,r)$?
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
147246
If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
63547
Euclid's Lemma and $\gcd(a,b)=1\Rightarrow \gcd(a^n,b^k)= 1$
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
138083
$\gcd(X^n - 1, nX^{n-1}) = 1$ in a field $K$ of characteristic $0$ or characteristic $p \nmid n$.
19046
Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
73972
How to prove that $\gcd(2n^3-14n+2,n+3) = \gcd(n+3,10)$?
136459
Prove ${n - 1 \choose k - 1} + {n - 2 \choose k - 1} + {n - 3 \choose k - 1} + \dots + {k - 1 \choose k - 1} = {n \choose k}$
116175
Show that $\gcd(3k+2,5k+3)=1$
48839
Show that the order of $a\times b$ is equal to $nm$ if gcd(n,m)=1