If $c\in \mathbb F_p^\times $, then $x^m-c=0$ has at most $m$ solution in $\mathbb F_p^\times $.
118916
How do I prove that a polynomial F[x] of degree n has at most n roots
51153
Number of solutions to $x^2\equiv a\pmod m$
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
146455
Compactness of the set of all unitary matrices in $M_2(\mathbb{C})$
151354
Why are there no non-trivial regular maps $\mathbb{P}^n \to \mathbb{P}^m$ when $n > m$?
135465
Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
144745
Proof of: If $x_0\in \mathbb R^n$ is a point of local minimum of $f$, then $\nabla f(x_0) = 0$.
8494
Proof Check: Number of elements of $\mathbb{F}_{p^{n}}$ of the form $a^{p}-a$ for some $a \in \mathbb{F}_{p^{n}}$.
7085
Prove that if the equation $x^{2} \equiv a\pmod{pq}$ has any solutions, then it has four solutions.
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
84697
Show that if $|f(z)| \leq M |z|^n$ then $f$ is a polynomial max degree n
73773
$C(M)=\{A\in M_n(\mathbb{C}) \mid AM=MA\}$ is a subspace of dimension at least $n$.
142725
The general solution of $x^a = a^x$ for real $a >0$
135511
$M_a =\{ f\in C[0,1] |\ f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated in $C[0,1]$?
134442
Can a matrix in $\mathbb{R}$ have a minimal polynomial that has coefficients in $\mathbb{C}$?
15314
Number of solutions to $x^n \equiv 1 \mod p$