If $(6,n)=1$, prove that $n^2-1$ is divisible by $24$.
15915
For any prime $p > 3$, why is $p^2-1$ always divisible by 24?
39716
Prove that $8(5)^n + 6(3)^{2n} - 80n - 14$ is divisible by $512$ for all $n \in \mathbb{N}$ by induction.
100892
Proving divisibility of $a^3 - a$ by $6$
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
124685
How to show $(mn)!$ is divisible by $(m!)^n$?
112541
Prove that $n^2 + 2^n$ is composite if $n\not\equiv3\pmod{6}$.
63416
Prove $(n^5-n)$ is divisible by 5 by induction.
17965
Prove 24 divides $u^3-u$ for all odd natural numbers $u$
143543
Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
50534
Prove that if $n^2$ is divided by 3, then also $n$ can also be divided by 3.
144132
The number $2^{3^n}+1$ is divisible by $3^{n+1}$ and not divisible by $3^{n+2}$.
82774
Prove by mathematical induction that $n^3 - n$ is divisible by $3$ for all natural number $n$
16472
Sum of First $n$ Squares Equals $\frac{n(n+1)(2n+1)}{6}$
141088
Proof : $2^{n-1}\mid n!$ if and only if $n$ is a power of $2$.
129238
Divisibility of $2^n - 1$ by $2^{m+n} - 3^m$.
139230
Prove that for every positive integer, this polynomial is divisible by 24.
32166
Prove: if $n\mid 7^n+6^n$ and $n>1$, then $13\mid n$