Find all natural numbers $n$ such that $2^n$ divides $3^n -1$
55437
When does $2^{n}$ divide $3^{n}-1$
33757
For what natural numbers is $n^3 < 2^n$? Prove by induction
119146
How to solve $n < 2^{n/8}$ for $n$?
12967
Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.
104965
Find $n$ such that polynomial is divisible
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$
44906
Use induction to prove that $2^n$ divides $(2n)!$ for any $n\in\mathbb{Z}_{\geq0}.$
49096
How can I prove $5^{3^n}+1$ is divisible by $3^{n+1}$
112147
Proving $9$ divides $n^3 + (n+1)^3 + (n+2)^3$
106847
Proof that $n^3+2n$ is divisible by $3$
142008
Find all natural numbers $n$ such that ${(n+1)}^{1/2}-{(n-1)}^{1/2}$ is rational
16407
$24\mid n(n^{2}-1)(3n+2)$ for all $n$ natural problems in the statement.
114873
Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
80144
Prove that $x-1$ divides $x^n-1$
9217
Find $n$ such that $x^2 + x + 1$ is a factor of $(x+1)^n - x^n - 1$.
110695
Divisor of $2^{2^n} + 1$ modulus $2^{n+1}$
78190
How to prove that for all natural numbers, $4^n > n^3$?