Does $\gcd(r, \sigma(r)) = 2r - \sigma(r)$ always hold when $r$ is deficient-perfect?
57281
Is Bezout's lemma enough to confirm the GCD of a number.
157155
How is HCF (c, d) = HCF (d, r), where c = dq +r (by Euclid's division lemma)?
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
125737
GCD( LCM(a,b) , LCM(a,c) ) = LCM(b, GCD(b,c)) , why?
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
11600
$\gcd(a,\operatorname{lcm}(b,c))=\operatorname{lcm}(\gcd(a,b),\gcd(a,c))$
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
41295
Divisibility, LCM and GCD for fractions (rationals)
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
83871
GCDs in integral domains are unique up to unit factors (associates)
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
14210
Fibonacci divisibilty properties $ F_n\mid F_{kn},\,$ $\, \gcd(F_n,F_m) = F_{\gcd(n,m)}$
114254
Zero divisors in $A[x_1,x_2,\dots,x_r]$
14693
$d = \gcd(c,m),\ ac≡bc\pmod{\! m}\Rightarrow a≡b\pmod {\!m/d}\ $ [Congruence Cancellation & Division Rule]
55673
Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?