Prove that n is a prime number if and only if $(n−2)! \equiv 1 \pmod n$.
123033
Showing a number $n$ is prime if $(n-2)! \equiv 1 \pmod n$
100984
Prove that if prime $p$ divide $a_{2k}-2$, then $p$ divide also $a_{2k+1}-1$.
6700
An Olympiad problem in prime numbers :can we proof that "n" is prime in this case "
15348
prime divisor of $3n+2$ proof
50781
$(n+1)$th prime $p_{n+1}$ less than or equal to $p_1p_2\dots p_n+1$
34692
Prove if $ p$ is a prime of the form $3n+1$, then $p$ is also of the form $6m+1$
65511
Proving the following false: $f(x)=2x+1$ produces a prime number if and only if x is prime
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?
143772
How can I algebraically prove that $2^n - 1$ is not always prime?
123296
Determine whether a number is prime
54547
Prove this number must be a prime number or 1.
2218
Prove that $(n-1)! \equiv -1 \pmod{n}$ iff $n$ is prime [Wilson's Theorem]
92737
primes whose difference is a multiple of $n$
75733
Divisibility of prime numbers
37093
If p is an odd prime, prove that $1^2 \times 3^2 \times 5^2 \cdots  \times (p-2)^2 \equiv (-1)^{(p+1)/2}\pmod{p}$
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$