If $\gcd (a,n) = 1$, how can we prove that $\gcd(a + kn, n) = 1$?
190
Why $\gcd(qb+r,b)=\gcd(b,r)$?
149993
Use the Euclidean algorithm to prove that gcd(na, nb) = n gcd(a, b).
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
52546
How can I find the possible values that $\gcd(a+b,a^2+b^2)$ can take, if $\gcd(a,b)=1$
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
42780
Show that if $a^{n-1} \equiv 1 \pmod{n}$ for all $a$ such that $\gcd(n,a) = 1$, then $a^{n} \equiv a \pmod{n}$ for all $a$.
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
83738
Prove $(k,n+k)=1$ iff $(k,n)=1$
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
7151
Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
14783
A Number Theory problem (GCD)
147079
$\gcd\left(\binom{n}{k},n\right)>1$ for nontrivial values?
128199
Proving gcd(a, a+2) is 1 or 2 for every integer a?
110313
Prove that $\gcd(f(x),g(x)) = 1$.
59566
Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$