$n^2 (n^4 - 1)$ is divisible by 60
105854
Prove $n^2(n^4-1)$ is divisible by 60 using Mathematical Induction.
35052
Prove that if $m^2 + n^2$ is divisible by $4$, then both $m$ and $n$ are even numbers.
122577
Prove that $(n^3 - 1)n^3(n^3 + 1)$ is divisible by $504$
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
80365
Prove that $n$ is divisible by $6$
107725
Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$
119891
Divisibility and the Fibonacci sequence
12729
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
3500
Compositeness of $n^4+4^n$
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
117167
$3^{n+1}$ divides $2^{3^n}+1$
20504
$\forall m,n \in \Bbb N$ : $\ 56786730\mid mn(m^{60}-n^{60})$
127833
Proving that $7^n(3n+1)-1$ is divisible by 9
125040
Show by induction : $n^7-n$ is a multiple of 7
280
Prove by induction that $5^n - 1$ is divisible by $4$.
72511
If $n$ is an odd natural number, then $8$ divides $n^{2}-1$