Proving $6^n - 1$ is always divisible by 5 by direct proof, not induction
120227
Proving $6^n - 1$ is always divisible by $5$ by induction
68480
Proof by Induction: Prove that $2^n > n^2$, for all natural numbers greater than or equal to $5$
44906
Use induction to prove that $2^n$ divides $(2n)!$ for any $n\in\mathbb{Z}_{\geq0}.$
134149
$z^n=(z+1)^n=1$, show that $n$ is divisible by $6$.
12729
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
130093
Prove by Induction : $n < 2^n$
19701
Prove $5\mid2^{4n}-1$ by induction
136700
Proving divisibility of expression using induction
31344
Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction
124240
Inductive proof of $\,9 \mathrel| 4^n+6n-1\,$ for all $\,n\in\Bbb N$
24053
How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
49299
Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
46741
Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra
31890
Prove using induction that from a set of $n+1$ numbers from $\{1,2,..2n\}$, at least one number will evenly divide another.
8366
Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
42526
The product of $n$ consecutive integers is divisible by $ n!$ (without using the properties of binomial coefficients)