$p$ a prime and I want to show $p^n-1 \mid p^m-1$ iff $n \mid m$
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
157884
For any prime $p>3$ show that 3 divides $2p^2+1$
50781
$(n+1)$th prime $p_{n+1}$ less than or equal to $p_1p_2\dots p_n+1$
12365
Show that every prime $p>3$ is either of the form $6n+1$ or of the form $6n+5$
32618
Suppose $p$ is a prime number such that $(p-1)/4$ and $(p+1)/2$ are also primes. Show that $p=13$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
106767
$|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
71788
Prove existence of multiplicative inverse modulo p when p is prime
130846
Prove or disprove: If $a \in \mathbb{Z}$, $a > 0$, and $p$ is a prime such that $p^4 \mid a^3$, then $p^2 \mid a$.
140830
Show $\,p\mid 9^q -1 \implies q\mid p-1$ for odd primes $p$ and $q$
21629
Using Fermat's Little Theorem Prove if $p$ is prime, prove $1^p + 2^p + 3^p +...+(p-1)^p \equiv 0 \bmod{p}$
131385
How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime
108380
Assume $P$ is a prime ideal s.t. $K \subset P$, show $f(P)$ is a prime ideal
113763
Let $p$,$\ q$ be prime numbers and $n\in \mathbb{N}$ such that $p \nmid n-1$. If $p \mid n^q-1$, then $q \mid p-1$.
62732
Prove：$x^d-1 \mid x^n-1$ iff $d \mid n$.
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too
65826
Find a prime number $p$ and an integer $b<p$ such that $p$ divides $b^{p−1}−1$.