Show that $(2^p-1,2^{q-1}-1)=2^{(p,q-1)}-1$
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
108318
counting proof for $\sum_{k=0}^{n-1} 2^{k} = 2^n - 1$
4970
For $n \geq 2$, show that $n \nmid 2^{n}-1$
110752
$g^\frac{p-1}{2} \equiv -1 \ (mod \ p)$
68561
How to show $\lceil ( \sqrt3 +1)^{2n}\rceil$ where $n \in \mathbb{ N}$ is divisible by $2^{n+1}$
51706
If $(k,l) = 1$, show that $(b_2k-b_1l, a_1l-a_2k) = 1$ for $a_1b_2-a_2b_1=1$
124131
Show that $(x-1)^2$ is a factor of $x^n -nx +n-1$
3109
Prove that $(p+q)^m \leq p^m+q^m$
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
88656
For $p$ prime, show that $\Phi_{p^n}(x) = 1 + x^{p^{n-1}} + x^{2p^{n-2}} + \dots +x^{(p-1)^{p^n-1}}$
55428
Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$
73238
Show that $a^{q-1} \equiv 1 \pmod{pq}$
145214
Showing the power set is equinumerous to ${}^X2$
134348
When is $(p - 1)! + 1$ a power of $p$?
148458
$x^p-x \equiv x(x-1)(x-2)\cdots (x-(p-1))\,\pmod{\!p}$
27784
Proving that $\left(\mathbb Q[\sqrt p_1,\dots,\sqrt p_n]:\mathbb Q\right)=2^n$ for distinct primes $p_i$.
119436
Proving $2^n\leq 2^{n+1}-2^{n-1}-1$ for all $n\geq 1$ by induction