$a,r,m\in \mathbb{Z^+}$ prove that $(a^r-1)\mid (a^m-1)\Leftrightarrow r\mid m$
1448
$x^a - 1$ divides $x^b - 1$ if and only if $a$ divides $b$
157711
Number Theory: Prove that $m | \phi(a^m - 1)$
60777
Prove $\, a_1 \Bbb Z \cap \dotsb \cap a_r \mathbb{Z} = {\rm lcm}(a_1, \ldots, a_r) \Bbb Z$
53857
Showing $\sup \{ \sin n \mid n\in \mathbb N \} =1$
57670
Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$
106584
If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$
64096
Prove that $||z_1|-|z_2|| \leq |z_1-z_2|$.
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
9846
Prove $n-m \mid n^r - m^r\,$ [Factor Theorem, monomial case]
18914
How prove this $A=\left(B-\frac{1}{110}I\right)^T\left(B+\frac{1}{110}I\right)$
43913
Prove that if $A^*+A=AA^*$ then $A$ is normal
114867
Prove $\forall n\geq 2,n\in\mathbb{Z}$, $(n+1)\mid(n^3+1)$
145041
Given that $p$ is a prime and $p\mid a^n$, prove that $p^n\mid a^n$.
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
76100
Showing that $\left\langle a,b \mid abab^{-1}\right\rangle \cong \pi_1(K) \cong \left\langle c,d \mid c^2 d^2 \right\rangle$
22093
How to show $a^{2^n}+1 \mid a^{2^m}-1$?
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$