prove by induction that $(a^n - b^n)$ is a multiple of $(a - b)$ for $n \geq 1$
2522
Why is $a^n - b^n$ divisible by $a-b$?
121874
Use Induction to prove that for all $n \in \mathbb{N}, (x^n + \frac{1}{x^n}) \in \mathbb{Z}$ if $x+\frac{1}{x}\in\mathbb{Z}$.
115459
Proving this $F_{n+1} \cdot F_{n-1} - F^2_n = (-1)^n$ by induction
62177
Prove that: $2^n < n!$ Using Induction
10629
How to prove $4(n!)>2^{n+2}$ for $ n\geq 4$ with induction
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
30783
Prove inequality $n<3^n$ using mathematical induction
139269
Prove that $2n-3\leq 2^{n-2}$ , for all $n \geq 5$ by mathematical induction
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
22073
Prove by induction that $n^2<n!$
45914
Proving that $n!≤((n+1)/2)^n$ by induction
10604
Prove $3^n > n^2$ by induction
88995
Prove that $a^n-b^n = (a-b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})$.
61117
Prove by induction: $n! \ge 2^{(n-1)}$ for any $n \ge 1$
134202
Proof by Induction - Math
108698
proof using the mathematical induction
8609
Prove by induction that $n!>2^n$