if $n>5$ is prime,prove $(n-1)|(n-2)!$
9319
If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.
51382
Proving that either $2^n-1 $ or $ 2^n+1$ is not prime
143543
Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
72600
Proof that $n!\leq {(\frac{n+1}{2})}^{n}$
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 $q \mid p-1$.
100558
Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
88144
Induction Proof $n! < n^n$
131385
How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime
137457
Use mathematical induction to prove that any integer $n\ge2$ is either a prime or a product of primes.
102889
If $2^n - 1$ is prime from some integer $n$, prove that n must also be prime.
62177
Prove that: $2^n < n!$ Using Induction
118383
If $n = 51! +1$, then find number of primes among $n+1,n+2,\ldots, n+50$
26503
Suppose that $p$ ≥ $q$ ≥ $5$ are both prime numbers. Prove that 24 divides ($p^2 − q^2$)
79208
Is the number $-1$ prime?
129302
Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
26514
Prove that if $n$ is a composite, then $2^n-1$ is composite.
22073
Prove by induction that $n^2<n!$