Gcd number theory proof: $(a^n-1,a^m-1)= a^{(m,n)}-1$
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
112031
Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
92630
How to prove $\gcd(a^m,b^m) = \gcd(a,b)^m$ using Bézout's Lemma
154133
Flawed proof by induction that $a^{n-1}=1$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
32344
Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
20477
Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$
31895
Prove that if $a$ and $b$ are odd, coprime numbers, then $\gcd(2^a +1, 2^b +1) = 3$
128199
Proving gcd(a, a+2) is 1 or 2 for every integer a?
107397
Algebraic proof for the identity $\sum_{k=0}^m(-1)^{m-k}{{n \choose {k}}}= {{n-1}\choose m}$
82938
$\gcd(a,b)=1, x^a = y^b\Rightarrow x = n^b$, $ y = n^a$ for an integer $n$.
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
63547
Euclid's Lemma and $\gcd(a,b)=1\Rightarrow \gcd(a^n,b^k)= 1$
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
157711
Number Theory: Prove that $m | \phi(a^m - 1)$