Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
108382
Prove $x^n-1$ is divisible by $x-1$ by induction
100558
Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
148330
Induction Proof for $F_{2n} = F^2_{n+1} - F^2_{n-1}$
5841
Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
124131
Show that $(x-1)^2$ is a factor of $x^n -nx +n-1$
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$
36906
Prove that $x^n+x^{-n} \in \mathbf{N}$ if $x+\frac1x \in \mathbf{N}$
100375
Prove that ${\sqrt {n} }^{\sqrt {n+1}} > {\sqrt {n+1}}^{\sqrt {n}}$.
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
55266
Prove that $(n+1)^{n-1}<n^n$
121544
Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
20964
Proof that $n^2 < 2^n$
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$