Proving that $\gcd(n!,\ n+1)=1$ or $n+1$
9319
If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
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 $a$.
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
7090
Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
116175
Show that $\gcd(3k+2,5k+3)=1$
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
66785
Find $\gcd(p^n-1,p^m+1)$.
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power