If $n,m\in\mathbb{N}$ and $n$ is odd, prove that $\gcd(2^n-1,2^m+1)=1$.
51858
Showing $\gcd(2^m-1,2^n+1)=1$
8366
Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
82938
$\gcd(a,b)=1, x^a = y^b\Rightarrow x = n^b$, $ y = n^a$ for an integer $n$.
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
122096
Find $GCD(n^2+1,n+1)$
139833
Prove that $\gcd(M, N)\times \mbox{lcm}(M, N) = M \times N$.
20003
Prove for positive integers a,b,c and d (where b does not equal d), if gcd(a,b) = gcd(c,d) = 1, then a/b + c/d is not an integer
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
69967
How to prove $\gcd(a^m-b^m,a^n-b^n) = a^{\gcd(m,n)} - b^{\gcd(m,n)} $?
158563
If $m^4+4^n$ is prime, then $m=n=1$ or $m$ is odd and $n$ even
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
45037
Show $(2^m-1,2^n+1)=1$ if $m$ is odd
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$