Let $a, m, n\in\mathbb{N^{*}}$ With $m>n$. Show ${(a^{2^m}-1,a^{2^n}+1)=a^{2^n}+1}$
22093
How to show $a^{2^n}+1 \mid a^{2^m}-1$?
8609
Prove by induction that $n!>2^n$
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$
55266
Prove that $(n+1)^{n-1}<n^n$
88995
Prove that $a^n-b^n = (a-b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})$.
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
36602
$a^m=b^m$ and $a^n=b^n$ imply $a=b$
127293
Prove that $(a-b) \mid (a^n-b^n)$
70827
Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
110662
Show that $P(\mathbb{N})$ is equivalent to $2^\mathbb{N}$
3109
Prove that $(p+q)^m \leq p^m+q^m$
4970
For $n \geq 2$, show that $n \nmid 2^{n}-1$
112031
Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
83662
Prove that $ a $ divides $1^{a^{n}} + 2^{a^{n}} + ... + (a-1)^{a^{n}}$?