Showing $2^n -1$ is composite when n is composite
26514
Prove that if $n$ is a composite, then $2^n-1$ is composite.
141088
Proof : $2^{n-1}\mid n!$ if and only if $n$ is a power of $2$.
22093
How to show $a^{2^n}+1 \mid a^{2^m}-1$?
65757
Prove that $n! + k$ is a composite number
9920
$(n^2 - 1)!$ is a multiple of $(n!)^n$
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
9319
If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.
143772
How can I algebraically prove that $2^n - 1$ is not always prime?
123117
Is it possible to find $n-1$ consecutive composite integers
103854
Showing that $Q_n=D_n+D_{n-1}$
121880
How to show that $|D_{2n}| = 2n$ via the presentation?
142666
Algebric proof for the identity $n(n-1)2^{n-2}=\sum_{k=1}^n {k(k-1) {n \choose k}}$
71014
Prove that 2(nC0+nC2...nC$\frac{(N-1)}{2}$=$2^n$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
105671
Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$
135614
Show that $2^n > n^2$ whenever n>4.
55742
Showing that $f_{2n+1}=f_{n+1}^2+f_n^2$.