Proving $x^n + x^{n-1} + \ldots + 1$ is reducible for $n$ composite
135747
Prove $x^{rs}-1=(x^s-1)(x^{s(r-1)}+...+x^s+1)$
69136
factorization of a^n+1?
111298
Direct Proof that $1 + 3 + 5 + \cdots+ (2n - 1) = n\cdot n$
16035
Irreducibility of $X^{p-1} + \cdots + X+1$
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
111316
PROVE if $x \ge-1 $then $ (1+x)^n \ge 1+nx $ , Every $n \ge 1$
51952
Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
138275
Show $100+t$ is reducible in $\mathbb{Z}[[t]]$
74224
On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
62342
$x_1 \cdot \dots \cdot x_n=1 \implies x_1 + \dots + x_n \ge n$
85459
$x^3+x+1$ irreducible over $\mathbb{F}_2$, $\theta$ root, compute powers of $\theta$
101057
Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
3500
Compositeness of $n^4+4^n$
81377
Show that $x^n + x + 3$ is irreducible for all $n \geq 2.$