$(a^{2^n}+1,a^{2^m}+1)=1 or 2$
25034
Fermat numbers are coprime
24572
Does $n \mid 2^{2^n+1}+1$ imply $n \mid 2^{2^{2^n+1}+1}+1$?
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
41300
Show $(x+y)^a > x^a + y^a$ for $x,y>0$ and $a>1$
70625
Prove By Induction $1 + 1/2 + 1/3 + ... + 1/(2^n) ≥ 1 + n/2$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
119436
Proving $2^n\leq 2^{n+1}-2^{n-1}-1$ for all $n\geq 1$ by induction
45037
Show $(2^m-1,2^n+1)=1$ if $m$ is odd
146093
Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
106584
If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
51858
Showing $\gcd(2^m-1,2^n+1)=1$
74222
If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
18477
$(W_1+W_2+\cdots+W_n)^a \leq W_1^a +\cdots + W_n^a$ for $n$ integer, $n\geq 2$, $W\gt 0$ and $a$ constant, real, $0\lt a\lt 1$
83662
Prove that $ a $ divides $1^{a^{n}} + 2^{a^{n}} + ... + (a-1)^{a^{n}}$?
112031
Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.