Prove that if $gcd(a, b)=d$ then $gcd(a^2, b^2 )=d^2$
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
107095
Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
147246
If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
20477
Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$
121156
Prove that: $\gcd[a,b,c]=\frac{abc.\operatorname{lcm}(a,b,c)}{\operatorname{lcm}(a,b)\operatorname{lcm}(a,c)\operatorname{lcm}(b,c)}$
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
118809
If $a$ divides $bc$ and $\gcd(a,b) = d$ then $\frac a d$ divides c