Show that $n^3+(n+1)^3+(n+2)^3$ is divisible by $9$
112147
Proving $9$ divides $n^3 + (n+1)^3 + (n+2)^3$
40896
What is the largest positive $n$ for which $n^3+100$ is divisible by $n+10$
12729
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
87379
How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
63553
Show that $\frac{1}{(n+1)!}(1+\frac{1}{(n+1)}+\frac{1}{(n+1)^2}+\frac{1}{(n+1)^3}+\cdots)=\frac{1}{n!n}$
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$
35342
Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
38904
Prove that $(a + b + c)^{13}$ is divisible by $abc$ if $b|a^3$, $c|b^3$ and $a|c^3$.
122019
Prove by mathematical induction that $2^{3^n}+1$ is divisible by $3^{n+1}$
63416
Prove $(n^5-n)$ is divisible by 5 by induction.
127833
Proving that $7^n(3n+1)-1$ is divisible by 9
15631
Show that $11^{n+1}+12^{2n-1}$ is divisible by $133$.
117969
Suppose $n$ divides $3^n + 4^n$. Show that $7$ divides $n$.
134149
$z^n=(z+1)^n=1$, show that $n$ is divisible by $6$.
89175
Proof of $(a+b)^{n+1}$
124685
How to show $(mn)!$ is divisible by $(m!)^n$?