Prove for $k>5$ prime, $(k-1)!+1$ has at least $2$ **different** prime divisors.
134348
When is $(p - 1)! + 1$ a power of $p$?
37947
Prove that if a number $n > 1$ is not prime, then it has a prime factor $\le \sqrt{n}$.
130615
divisibility of binomial coefficients by primes
50413
Proof: if $p$ is prime, and $0<k<p$ then $p$ divides $\binom pk$
111490
Proof that every number has at least one prime factor
5841
Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
70308
Prove that if $p$ and $p+2$ are both prime integers greater than $3$, then $6$ is a factor of $p+1$.
132587
Prove that the product of coprimes must be congruent to $-1$ or $1 \pmod{m}$
14724
For primes $p≡3\pmod 4$, prove that $[(p−1)/2]!≡±1\pmod p$.
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
15348
prime divisor of $3n+2$ proof
57944
Euler's Formula application for distinct odd primes with gcd 1
56229
On the difference between consecutive primes
13739
For all $n>2$ there exists a prime number between $n$ and $ n!$
64148
If $p$ and $q$ are distinct primes and $a$ be any integer then $a^{pq} -a^q -a^p +a$ is divisible by $pq$.