Proof that $(2^m - 1, 2^n - 1) = 2^d - 1$ where $d = (m,n)$
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
119436
Proving $2^n\leq 2^{n+1}-2^{n-1}-1$ for all $n\geq 1$ by induction
66145
>Prove that $\frac d {dx} x^n=nx^{n-1}$ for all $n \in \mathbb R$.
22093
How to show $a^{2^n}+1 \mid a^{2^m}-1$?
55266
Prove that $(n+1)^{n-1}<n^n$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
10917
Give a combinatorial proof: $ n(n+1)2^{n-2} = \sum_{k=1}^{n}k^2\binom{n}{k} $
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
20964
Proof that $n^2 < 2^n$
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
52206
How to prove with double counting technique that $1+2+\dots+2^n=2^{n+1} -1$?
121706
Show $\text{det}(A)$ is divisible by $2^{n-1}$
88995
Prove that $a^n-b^n = (a-b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})$.
130223
Proving a special case of the binomial theorem: $\sum^{k}_{m=0}\binom{k}{m} = 2^k$
98514
Prove by induction that the number of derangements of length $n$ is $D_n = (n-1)(D_{n-1}+D_{n-2}), n>2$
345
Proving $ \sum _{k=0} ^m \binom nk \binom{n-k}{m-k} = 2^m \binom {n}{m}$.