$1+n!=m^{2}$ for some n,m$\in\mathbb{N}$
19588
$n!+1$ being a perfect square
114506
Expansion of $(1+\sqrt{2})^n$
137967
Are there $a,b \in \mathbb{N}$ that ${(\sum_{k=1}^n k)}^a = \sum_{k=1}^n k^b $ beside $2,3$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
88144
Induction Proof $n! < n^n$
10629
How to prove $4(n!)>2^{n+2}$ for $ n\geq 4$ with induction
62177
Prove that: $2^n < n!$ Using Induction
63661
integers $n$ such that $(n-1)!+1$ is a power of $n$
4970
For $n \geq 2$, show that $n \nmid 2^{n}-1$
13330
Inductive Proof that $k!<k^k$, for $k\geq 2$.
8884
Find all natural numbers $n$ and $m$ for which $n^m=(n-1)!+1$
61117
Prove by induction: $n! \ge 2^{(n-1)}$ for any $n \ge 1$
59462
Prove that $n!=\prod_{k=1}^n \operatorname{lcm}(1,2,...,\lfloor n/k \rfloor)$ for any $n \in \mathbb N$
45914
Proving that $n!≤((n+1)/2)^n$ by induction
26011
To show that $2$ | $x^{2n} - x^n$, $n \in \mathbb{Z^+}$ is the following adequate?
70611
Prove by Mathematical Induction: $1(1!) + 2(2!) + \cdot \cdot \cdot +n(n!) = (n+1)!-1$
122932
When $(\mathbb{Q}(\zeta_n) : \mathbb{Q}) = 2$?