How can we prove that x^n - 1 always be a multiple of x - 1
80144
Prove that $x-1$ divides $x^n-1$
51896
Prove that: set $\{1, 2, 3, ..., n - 1\}$ is group under multiplication modulo $n$?
143543
Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
62732
Prove：$x^d-1 \mid x^n-1$ iff $d \mid n$.
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
114379
Show that number of solutions satisfying $x^5=e$ is a multiple of 4?
77076
Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
102524
$ 1^k+2^k+3^k+...+(p-1)^k $ always a multiple of $p$?
64457
Prove:$|x-1|+|x-2|+|x-3|+\cdots+|x-n|\geq n-1$
85525
Prove that $x^3+x+1$ splits in $Z_2[x]/(x^3+x+1)$
80242
Prove that $n^{2003}+n+1$ is composite for every $n\in \mathbb{N} \backslash\{1\}$
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
97805
$n+1$ is a divisor of $\binom{2n} {n}$
143067
Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.