$n!+1$ is composite for infinitely many odd $n$
135892
Understanding the proof for showing that there are infinitely many $n\in\mathbb{Z}^+$ such that $n!+1$ is divisible by at least two distinct primes
96027
Prove that if $a+b+c$ divides $abc$, then $a+b+c$ must be composite.
22367
How do I prove that for every positive integer $n$, there exist $n$ consecutive positive integers, each of which is composite?
140359
Can the sum of finitely many inverses of distinct odd integers $\geq 3$ be 1?
103538
Partitions of $n$ into distinct odd and even parts proof
140006
Are there infinitely many primes and non primes of the form $10^n+1$?
91285
Prove $a+b+c+d $ is composite
116361
Relationship between prime factorizations of $n$ and $n+1$?
52089
Group of $2n$ elements, $n$ odd, is not simple
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
27063
Prove that if n is an odd positive integer , then $n^2\equiv1\mod8$
112541
Prove that $n^2 + 2^n$ is composite if $n\not\equiv3\pmod{6}$.
19588
$n!+1$ being a perfect square
55266
Prove that $(n+1)^{n-1}<n^n$
9319
If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.
149241
What is the maximum number of consecutive composite numbers possible?
47720
Isomorphism from Natural numbers to the Odd Natural numbers