If $a $ divides $b$, then $(2^a-1) $ divides $(2^b-1)$
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
90486
If $(A-B)^2=O_2$ then $\det(A^2 - B^2)=(\det(A) - \det(B))^2$
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
88995
Prove that $a^n-b^n = (a-b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})$.
77806
Proving if $a$ is not a multiple of prime $p$, then an integer $b$ exists such that $p^b - 1$ is a multiple of $a$
48404
If $a$ and $b$ are integers such that $9$ divides $a^2 + ab + b^2$ then $3$ divides both $a$ and $b$.
33866
Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
82097
If $A \succeq B$, is it true that $B^{-1} \succeq A^{-1}$?
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
2522
Why is $a^n - b^n$ divisible by $a-b$?
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
118809
If $a$ divides $bc$ and $\gcd(a,b) = d$ then $\frac a d$ divides c
40626
Suppose that $ a,b \in \mathbb{Z}$ If 4 divides $ a^2 + b^2$, then $a$ and $b$ are not odd.
19202
$\mathbb{F}_{p^d}\subseteq\mathbb{F}_{p^n}$ if and only if $d$ divides $n$