Let a,b,c $\in\mathbb{Z}$ such that a|k, b|k and gcd (a,b)=1. Prove that ab|k.
1991
If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
106416
If $n,m \in \mathbb{N}$ then there are $c,d$ such that $cd = (m,n)$, $(c,d) = 1$ and $(m/c,n/d) = 1$.
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
17677
Prove or show a counter example for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
156966
Prove that if $b = dk$ where $gcd(m, a) = d$, there are $d$ solutions to $ax \equiv b \mod m$
25907
Show $a\Bbb Z+b\Bbb Z = \gcd(a,b)\Bbb Z$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
32344
Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$