How to prove that $n^5 - n$ is a multiple of $5$?
63416
Prove $(n^5-n)$ is divisible by 5 by induction.
55266
Prove that $(n+1)^{n-1}<n^n$
152084
Binomial-Theorem proof
280
Prove by induction that $5^n - 1$ is divisible by $4$.
20964
Proof that $n^2 < 2^n$
153594
When is $1^5 + 2^5 + \ldots + n^5$ a square?
146867
Combinatorial Proof Of A Number Theory Theorem--Confusion
110722
$n$ and $n^5$ have the same units digit?
43010
Prove that for every n ∈ Z, there exist a, b ∈ Z such that $n = 5a + 2b$.
143510
Prove that $n=\frac{5^{125}-1}{5^{25}-1}$ is a composite number
14581
How do we prove $n^n \mid m^m \Rightarrow n \mid m$?
20705
On equations $m^2+1=5^n$
133017
Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
50894
Prove that $6$ divides $n(n + 1)(n + 2)$
35326
There are infinitely many $N$ such that $\frac{N}{2}$ is a perfect square, $\frac{N}{3}$ is a perfect cube, and $\frac{N}{5}$ is a perfect fifth power
30620
For which natural n is $3^n+5^n$ divisible by $3^{n-1}+5^{n-1}$?
116054
The number $(3+\sqrt{5})^n+(3-\sqrt{5})^n$ is an integer