prove that $n$ is prime or $n=4$ when $n|4((n−1)!+1)$
9319
If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.
137457
Use mathematical induction to prove that any integer $n\ge2$ is either a prime or a product of primes.
111037
Consider numbers of the type $n=2^m+1$. Prove that such an n is prime only if $n=F_K$ for some $ k \in N$, where $F_k$ is a Fermat Prime.
154475
Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number
95889
Prove that $\gcd(n! + 1, 3n! + 1) = 1$, $\forall n \in \mathbb{N}$, $n \geq 2$.
105442
Show that any prime divisor of $x^4+x^3+x^2+x+1$, with $x\in\mathbb{N}$, is $5$ or $1$ mod $5$
153123
Proving by induction $4^n  0$
22023
Infinitely number of primes in the form $4n+1$ proof
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
3043
Prove $n!>2^n$ for $n\geq4$ using induction.
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
45914
Proving that $n!≤((n+1)/2)^n$ by induction
2218
Prove that $(n-1)! \equiv -1 \pmod{n}$ iff $n$ is prime [Wilson's Theorem]
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
68688
n-th prime number is less than $4^n$
34954
If $11..11$($n$ times 1) is prime, prove that $n$ is also prime
111490
Proof that every number has at least one prime factor