Divisibility via Induction: $8^n\mid (4n)!$
90789
Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
11867
Prove by induction that $n < 2^n$ for all $n \ge 1$
150462
Prove by induction that for every $n \ge 0$ the term $2^{2n+1} - 9n^2 + 3n -2$ is divisible by $54$
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
31292
Divisibility Proof with Induction - Stuck on Induction Step
11470
Divisibility of integers
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
85941
Proof by induction that $n^3 - n$ is divisible by $6$
70386
Proof by induction: $2^n > n^2$ for all integer $n$ greater than $4$
78726
Prove via mathematical induction that $4n < 2^n$ for all $ n≥5$.
100256
Proof by induction on a rooted tree with even number of vertices
28957
Verifying that $2^{44}-1$ is divisible by $89$
63416
Prove $(n^5-n)$ is divisible by 5 by induction.
56512
Divisibility is transitive: $\ a\mid b\mid c\,\Rightarrow\ a\mid c$
8609
Prove by induction that $n!>2^n$
12729
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?