Let $n \ge 2$. If $n$ divides $3^n + 4^n$, prove that $7$ divides $n$.
117969
Suppose $n$ divides $3^n + 4^n$. Show that $7$ divides $n$.
50894
Prove that $6$ divides $n(n + 1)(n + 2)$
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
105671
Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
17194
$6^{(n+2)} + 7^{(2n+1)}$ is divisible by $43$ for $n \ge 1$
78985
Prove that: $\sqrt{2\sqrt{3\sqrt{4\cdots\sqrt{n}}}}<3,\,\forall n\in\mathbb N.$
91914
Prove that for the Fibonacci sequence $(F_n)$, $F_n$ divides $F_{2n}$.
130488
Prove by induction that $3\mid n^3 - n$
40131
If n is such that every element $(\mathbb{Z}/n\mathbb{Z})^{\times}$ is a root of $x^2-1$. Prove that $n$ divides 24.
128306
Show that for all $n ∈ Z$, $2n^3 + 3n^2 + n$ is divisible by both 2 and 3.
44906
Use induction to prove that $2^n$ divides $(2n)!$ for any $n\in\mathbb{Z}_{\geq0}.$
21100
Simple Proof by induction: $9$ divides $n^3 + (n+1)^3 + (n+2)^3$
12729
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
10604
Prove $3^n > n^2$ by induction
4077
Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.