Prove that $ n^3 + 5n$ is divisible by 6 for all $n\in \textbf{N}$
17965
Prove 24 divides $u^3-u$ for all odd natural numbers $u$
62100
Show that $n^3-n$ is divisible by $6$ using induction
29963
$6$ divides $a+b+c$ if and only if $6$ divides $a^{3}+b^{3}+c^{3}$
30620
For which natural n is $3^n+5^n$ divisible by $3^{n-1}+5^{n-1}$?
17194
$6^{(n+2)} + 7^{(2n+1)}$ is divisible by $43$ for $n \ge 1$
124685
How to show $(mn)!$ is divisible by $(m!)^n$?
39716
Prove that $8(5)^n + 6(3)^{2n} - 80n - 14$ is divisible by $512$ for all $n \in \mathbb{N}$ by induction.
26336
Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
49501
Prove that : $(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)$ divisible by $12$
50670
Use Mathematical Induction to prove 6 divides $n(n+1)(2n+1)$
72557
Prove that $T(n) = T(n/3) + T2n/3) + 5n$ is $O(n log n)$
4077
Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
117761
When is $\binom{n}{k}$ divisible by $n$?
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$
122577
Prove that $(n^3 - 1)n^3(n^3 + 1)$ is divisible by $504$