If $\gcd(m,n) = 1$, show that $m^{φ(n)} + n^{φ(m)} ≡ 1 \mod{mn}$
125188
how to prove $m^{\phi(n)}+n^{\phi(m)}\equiv 1 \pmod{mn}$ where m and n are relatively prime?
116175
Show that $\gcd(3k+2,5k+3)=1$
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
88656
For $p$ prime, show that $\Phi_{p^n}(x) = 1 + x^{p^{n-1}} + x^{2p^{n-2}} + \dots +x^{(p-1)^{p^n-1}}$
72424
Suppose 1 ≤ k ≤ n − 1 and gcd(k, n) = 1. Prove that gcd(n − k, n) = 1
88124
$M,N\in \Bbb R ^{n\times n}$, show that $e^{(M+N)} = e^{M}e^N$ given $MN=NM$
59566
Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
5223
$\mathbb{Z}_m \times \mathbb Z_n$ is cyclic if and only if $\gcd(m,n)=1$
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
46147
Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
92630
How to prove $\gcd(a^m,b^m) = \gcd(a,b)^m$ using Bézout's Lemma
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
61825
Congruence class $[a]$ modulo $m$, $\gcd(x, m) = \gcd(a, m)$
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$