How to show that if p is prime and m,n are natural numbers then $p^m -1 | p^n -1$
1448
$x^a - 1$ divides $x^b - 1$ if and only if $a$ divides $b$
12365
Show that every prime $p>3$ is either of the form $6n+1$ or of the form $6n+5$
158563
If $m^4+4^n$ is prime, then $m=n=1$ or $m$ is odd and $n$ even
24403
Prove that $ n < 2^{n}$ for all natural numbers $n$.
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
5841
Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
45037
Show $(2^m-1,2^n+1)=1$ if $m$ is odd
39915
Let $n$ be an integer such that if $d | n$ then $d + 1 | n + 1.$ Show that $n$ is a prime number
145519
Prove that for any natural number $n>1$, we have $(2n)!<(n(n+1))^n$
78847
Bijection between Prime numbers and Natural numbers
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
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 $a$
88656
For $p$ prime, show that $\Phi_{p^n}(x) = 1 + x^{p^{n-1}} + x^{2p^{n-2}} + \dots +x^{(p-1)^{p^n-1}}$
116361
Relationship between prime factorizations of $n$ and $n+1$?
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
131141
Solutions to $p+1=2n^2$ and $p^2+1=2m^2$ in Natural numbers.