Number Theory Greatest Common Divisor proof
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
10966
gcd and lcm from prime factorization proof
96376
Why do we notate the greatest common divisor of $a$ and $b$ as $(a,b)$?
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
157508
prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
30752
Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
117098
Properties of the greatest common divisor: $\gcd(a, b) = \gcd(a, b-a)$ and $\gcd(a, b) = \gcd(a, b \text{ mod } a)$
135086
GCD of two numbers divided by their greatest common divisor is 1
48452
Proof that $\gcd$ divides $\operatorname{lcm}$
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$