Show that if a prime number $p|a^n$ then $p|a$
75733
Divisibility of prime numbers
84603
Prove that if $p$ is a prime such that $p^2+2$ is a prime then $p=3$.
146304
prove $(n)$ prime ideal of $\mathbb{Z}$ iff $n$ is prime or zero
7899
Show that if $p$ is prime then $\Bbb Z_p$ is a field
12365
Show that every prime $p>3$ is either of the form $6n+1$ or of the form $6n+5$
13739
For all $n>2$ there exists a prime number between $n$ and $ n!$
110662
Show that $P(\mathbb{N})$ is equivalent to $2^\mathbb{N}$
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 $a$
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
834
If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.
131488
Show that $p^3+4$ is prime
42292
Show that $a_n<\sqrt{2}$ for every $n\in\mathbb{N}$.
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
154475
Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number
36943
How to prove that $L=${$a^p$: p is prime} isn't regular?
33714
$p$ prime, $p\mid a^k \Rightarrow p^k\mid a^k$
154076
How to show this property of $\mathbb{RP}^{n}$.