Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
103854
Showing that $Q_n=D_n+D_{n-1}$
19202
$\mathbb{F}_{p^d}\subseteq\mathbb{F}_{p^n}$ if and only if $d$ divides $n$
49501
Prove that : $(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)$ divisible by $12$
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
100984
Prove that if prime $p$ divide $a_{2k}-2$, then $p$ divide also $a_{2k+1}-1$.
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$
66145
>Prove that $\frac d {dx} x^n=nx^{n-1}$ for all $n \in \mathbb R$.
143543
Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
62732
Prove：$x^d-1 \mid x^n-1$ iff $d \mid n$.
26215
Proof Verification: Let $D=\{ \frac{1}{n} \mid n\in\mathbb{N} \} \cup\{0\} \subset \mathbb{E}^1$. Prove that $D$ is compact.
55266
Prove that $(n+1)^{n-1}<n^n$
33866
Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
97805
$n+1$ is a divisor of $\binom{2n} {n}$
31344
Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction
59479
For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$