Proof about divisibility and greatest common divisor that doesn't use Bezout's formula
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
7090
Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
10966
gcd and lcm from prime factorization proof
74523
Proof by Cases involving divisibility
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
107095
Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
130944
Greatest common divisor of polynomials over $\mathbb{Q}$
40538
On determinants and common divisors
135086
GCD of two numbers divided by their greatest common divisor is 1
113152
Prove Principal Ideal Domain from Bezout's condition, and terminating divisibility chain
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
146980
Zero divisors of $\mathbb{Z}×\mathbb{Z}×\mathbb{Z}$
137369
Inductive proof of gcd Bezout identity (from Apostol: Math, Analysis 2ed)
157508
prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$