Prove that $n^{n-1} - 1$ is divisible by $(n-1)^2$
9997
For what powers $k$ is the polynomial $n^k-1$ divisible by $(n-1)^2$?
3611
How to prove $n^5 - n$ is divisible by $30$ without reduction
53866
Prove $ x^n-1=(x-1)(x^{n-1}+x^{n-2}+...+x+1)$
91197
Proving $n! \ge 2^{n-1 }$for all $n\ge1 $by mathematical Induction
120227
Proving $6^n - 1$ is always divisible by $5$ by induction
10191
Binomial theorem: divisibility by $n^2$
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$
115459
Proving this $F_{n+1} \cdot F_{n-1} - F^2_n = (-1)^n$ by induction
97805
$n+1$ is a divisor of $\binom{2n} {n}$
100558
Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$
59479
For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$
15631
Show that $11^{n+1}+12^{2n-1}$ is divisible by $133$.
80144
Prove that $x-1$ divides $x^n-1$