If $\,k\mid n^2-1\,$ for all $n$ coprime to $k$ then $k\mid 24\ $
40131
If n is such that every element $(\mathbb{Z}/n\mathbb{Z})^{\times}$ is a root of $x^2-1$. Prove that $n$ divides 24.
48655
Find all n such that : $3 \mid (n2^{n}+1)$
50894
Prove that $6$ divides $n(n + 1)(n + 2)$
87813
How to show that for all k, $k! \ge (k/2)^{k/2}$
26449
$|G|=24$ prove that $G$ is not simple
60804
About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
100558
Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
35553
If $n$ is composite, so is $2^n-1$
14581
How do we prove $n^n \mid m^m \Rightarrow n \mid m$?
151520
About the parity of the product $(a_1-1)(a_2-2)\cdots(a_n-n)$
32803
Prove that if b is coprime to 6 then $b^2 \equiv 1 $ (mod 24)
50614
If $4\mid a+bc$ and $6\mid b+ac$ prove that $2\mid a^2-b^2$
146093
Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
17047
Prove that if n is even then $n^2$ is even and if n is odd then $n^2$ is odd?
7491
How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?
33344
A different way to show that $a^k-1 \mid a^n-1$ if $k\mid n$?
18018
Proving that $4 \mid m - n$ is an equivalence relation on $\mathbb{Z}$