$x^{2}+x+1$ is a factor of $(x+1)^{n} - x^{n} - 1$, whenever
9217
Find $n$ such that $x^2 + x + 1$ is a factor of $(x+1)^n - x^n - 1$.
16035
Irreducibility of $X^{p-1} + \cdots + X+1$
135747
Prove $x^{rs}-1=(x^s-1)(x^{s(r-1)}+...+x^s+1)$
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
121874
Use Induction to prove that for all $n \in \mathbb{N}, (x^n + \frac{1}{x^n}) \in \mathbb{Z}$ if $x+\frac{1}{x}\in\mathbb{Z}$.
156356
Proof that $x^n+\frac{1}{x^n}\in \mathbb Z$ by complete induction
143236
$ S_{n}=\frac{x}{x+1}+\frac{x^2}{(x+1)(x^2+1)}+...........+\frac{x^{2^{n}}}{(x+1)(x^2+1)...(x^{2^{n}}+1)}$
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
111316
PROVE if $x \ge-1 $then $ (1+x)^n \ge 1+nx $ , Every $n \ge 1$
26336
Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
21439
For which $k\in \Bbb N$ does $x^2+x+1$ divide $ (x + 1)^{2k}+x^{2k} + 1$?
117816
Is $\frac{x^2+x}{x+1}$ a polynomial?
48211
When is $(a+b)^n \equiv a^n+b^n$?
113230
How can we factor $ q^4 + q^2 + 1$
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
37068
How could it possible to factorise $x^8-1$ in product of irreducibles in the rings $(\mathbb{Z}/2\mathbb{Z})[x]$ and $(\mathbb{Z}/3\mathbb{Z})[x]$?
70308
Prove that if $p$ and $p+2$ are both prime integers greater than $3$, then $6$ is a factor of $p+1$.