$x^d-1|x^n-1$ iff $d|n$
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
106585
Show $d_{1}(x_{n},x)\rightarrow{0}$ if and only if $d_{2}(x_{n},x)\rightarrow{0}$.
1712
$ d_1,d_2\mid n\iff {\rm lcm}(d_1,d_2)\mid n\ $ [LCM Universal Property]
72410
If $\alpha_1,\alpha_2,\ldots,\alpha_n$ be the roots of the equation $x^n+1$
29935
If $a, b, c, d>0$ and $abcd=1$ prove that an inequality holds true
144439
For a $C^1$ function, the difference $|{g'(c)} - {{g(d)-g(c)} \over {d-c}} |$ is small when $|d-c|$ is small
150289
A number with an interesting property. $abcd=a^b c^d$
25419
If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
103246
Prove that a polynomial of degree $d$ has at most $d$ roots (without induction)
46746
How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?
55266
Prove that $(n+1)^{n-1}<n^n$
35553
If $n$ is composite, so is $2^n-1$
38568
Finding the number of zeros of $f(z) = z^n$ if $|f(z)| < 1 $ for all $z$ with $|z|=1$.
25471
Irreducibility of $x^n-x-1$ over $\mathbb Q$
100515
Prove that if $d$ divides $n$ then $φ(d)$ divide $φ(n)$ for $φ$ denotes Euler’s φ-function.
9217
Find $n$ such that $x^2 + x + 1$ is a factor of $(x+1)^n - x^n - 1$.