Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
155784
If $\gcd(a, b) = 1$ and if $ab = x^2$, prove that $a, b$ must also be perfect squares; where $a,b,x$ are in the set of natural numbers
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
72747
Proving gcd($a,b$)lcm($a,b$) = $|ab|$
128199
Proving gcd(a, a+2) is 1 or 2 for every integer a?
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
95889
Prove that $\gcd(n! + 1, 3n! + 1) = 1$, $\forall n \in \mathbb{N}$, $n \geq 2$.
130653
$p^2$ divides $ab$ and $\gcd(a,b)=1$. Show $p^2$ divides $a$ or $p^2$ divides $b$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
56612
Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$