If n = $\frac{a^{2p}-1}{a^2-1}$ where $a$ is an integer $>1$ and $p$ is an odd prime, then $n$ is pseudoprime to the base $a$.
43940
Showing that $n$ is pseudoprime to the base $a$
118629
$p,q$ odd primes, $q\mid a^p-1\Rightarrow q\mid a-1$ or $\,2p\mid q-1$
140948
Suppose $p$ and $q$ are odd primes and $p = q + 4a$ for some $a$. Prove that $(\frac ap) = (\frac aq)$ holds.
158563
If $m^4+4^n$ is prime, then $m=n=1$ or $m$ is odd and $n$ even
10861
Let$\ p_n$ be the$\ n$-th prime. Can you give me a proof for$\ \prod_{i=1}^\infty \frac{p_i-1}{p_i}=P\approx \frac{1}{11.0453}$?
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 $a$
42376
Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
68145
If $p$ is an odd prime and $k$ an integer with $0<k<p-1$ then $1^k + 2^k + \ldots + (p-1)^k$ is divisible by $p$
29572
Proof that $2^n-1$ does not always generate primes when primes are plugged in for $n$?
154475
Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number
154305
Let $\pi$ denote a prime element in $\mathbb Z[i], \pi \notin \mathbb Z, i \mathbb Z$. Prove that $N(\pi)=2$ or $N(\pi)=p$, $p \equiv 1 \pmod 4$
44857
Why the $(n+1)$th prime number cannot exceed the smallest prime divisor of $p_1\dotsc p_n + 1$
19761
Show for prime numbers of the form $p=4n+1$,  $x=(2n)!$ solves the congruence $x^2\equiv-1 \pmod p$. $p$ is therefore not a gaussian prime.
145752
Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?