Prove that $8(5)^n+6(3)^{2n}−80n−14$ is divisible by $512$ for all $n\in\mathbb{N}$ by induction.
39716
Prove that $8(5)^n + 6(3)^{2n} - 80n - 14$ is divisible by $512$ for all $n \in \mathbb{N}$ by induction.
130093
Prove by Induction : $n < 2^n$
82774
Prove by mathematical induction that $n^3 - n$ is divisible by $3$ for all natural number $n$
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
95141
$n^5-n$ is divisible by $10$?
27798
Prove that $ n^3 + 5n$ is divisible by 6 for all $n\in \textbf{N}$
9435
Prove that $1^2+2^2+\cdots+n^2=\frac{n(n+1)(2n+1)}{6}$ for $n \in \mathbb{N}$.
1837
Showing that $1^k+2^k + \dots + n^k$ is divisible by $n(n+1)\over 2$
116363
If $P(x^5)+xQ(x^5)+x^2R(x^5)=(x^4+x^3+x^2+x+1)S(x)$ , then prove that $P(x)$ is divisible by $x-1$
90789
Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
138846
Prove by induction that $3\mid n^4-n^2$ for all $n \in \mathbb{Z^+}$, $n\ge2$.
72511
If $n$ is an odd natural number, then $8$ divides $n^{2}-1$
80365
Prove that $n$ is divisible by $6$
128306
Show that for all $n ∈ Z$, $2n^3 + 3n^2 + n$ is divisible by both 2 and 3.
106847
Proof that $n^3+2n$ is divisible by $3$
122019
Prove by mathematical induction that $2^{3^n}+1$ is divisible by $3^{n+1}$