Prove $x^n-1$ is divisible by $x-1$ by induction
2522
Why is $a^n - b^n$ divisible by $a-b$?
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
26336
Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
88144
Induction Proof $n! < n^n$
19701
Prove $5\mid2^{4n}-1$ by induction
52113
Proof by Induction $\sum_{i=0}^{k-1} 2^i = 2^k-1$
50670
Use Mathematical Induction to prove 6 divides $n(n+1)(2n+1)$
66358
Prove by mathematical induction that $2n ≤ 2^n$, for all integer $n≥1$?
150462
Prove by induction that for every $n \ge 0$ the term $2^{2n+1} - 9n^2 + 3n -2$ is divisible by $54$
123195
Prove by induction that a^n+a^-n is an integer.
77076
Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
55273
Prove by mathematical induction that: $\forall n \in \mathbb{N}: 3^{n} > n^{3}$
81601
Prove that if $x$ is odd then $x^2 -1$ is divisible by $8$.
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
4077
Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.
26588
Prove by induction that $10^n -1$ is divisible by 11 for every even natural number
31344
Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction