If $d \mid n$ then $x^{q^d} - x \mid x^{q^n} - x$.
12134
divisibility question in abstract algebra over a field
97667
If $a<b$, $c<d$ then $a+c<b+d$?
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
138846
Prove by induction that $3\mid n^4-n^2$ for all $n \in \mathbb{Z^+}$, $n\ge2$.
131551
$pq\mid pn^q+qn^p+kn$ for some $k,\,$ if $p,q$ are primes
145041
Given that $p$ is a prime and $p\mid a^n$, prove that $p^n\mid a^n$.
103246
Prove that a polynomial of degree $d$ has at most $d$ roots (without induction)
48251
Prove that if $n \in \mathbb{N}$, then $\sum_{d|n}{(d(n))^3}=(\sum_{d|n}{d(n)})^2$ where $d(n)$ is the divisor function.
31724
How prove that $q \geq b+d$ for $ad-bc = 1$ and $\frac{a}{b} > \frac{p}{q} > \frac{c}{d}$?
118809
If $a$ divides $bc$ and $\gcd(a,b) = d$ then $\frac a d$ divides c
83752
If $p + q = 1$ prove that for any natural $n, m$ following is true: $(1 - p^n)^m + (1 - q^m)^n \ge 1$
83407
How to show that that $q \mid p-1$?
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
143545
If $(a_n)$ is Cauchy it has a subsequence $(a_{n_i})$ such that $d(a_{n_{i+1}},a_{n_i})<2^{-i}$ for all $i$.
141088
Proof : $2^{n-1}\mid n!$ if and only if $n$ is a power of $2$.
119118
Prove $n\mid \phi(2^n-1)$
4333
Prove that if $a+b+c+d=4$, then $(a^2+3)(b^2+3)(c^2+3)(d^2+3)\geq256$