Proving that $ \gcd(a,b) = as + bt $, i.e., $ \gcd $ is a linear combination.
3694
Show $GCD(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
422
If $\gcd(a,b)=1$, $\gcd(a,y)=1$ and $\gcd(b,x)=1$ then prove that $ax+by$ is prime to $ab$
72747
Proving gcd($a,b$)lcm($a,b$) = $|ab|$
43728
Proof via Group Theory : $\mathrm{lcm}(a,b) \cdot \gcd(a,b) = |ab|$
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
60842
if $a^2+b^2=c^2$ then $gcd(a,b)=gcd(a,c)=gcd(b,c)$.
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
103147
$\operatorname{gcd}(ab,a+b)=1$ if $a$ and $b$ are relatively prime
149993
Use the Euclidean algorithm to prove that gcd(na, nb) = n gcd(a, b).
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
190
Why $\gcd(qb+r,b)=\gcd(b,r)$?
69967
How to prove $\gcd(a^m-b^m,a^n-b^n) = a^{\gcd(m,n)} - b^{\gcd(m,n)} $?