Let $f(x)$ belong to $\mathbb{Z}_p[x]$. Prove that if $f(b)=0$, then $f(b^p)=0$.
65459
Roots of polynomials in field of prime characteristic p
136056
$ f:\mathbb C\rightarrow \mathbb C$ defined by $f(z)=0$, if $Re(z)=0$ or $Im(z)=0$ and $f(z)=z$, otherwise.
28949
Prove $f(x) = 0 $for all $x \in [0, \infty)$ when $|f'(x)| \leq |f(x)|$
62615
If F is a finite field, then $F^F=P_F$.
148813
Prove: $f: \mathbb{R} \rightarrow \mathbb{R}$ st for every $x \in \mathbb{R}$ there exists $n$ st $f^{(n)}(x) = 0$, f is a polynomial.
135511
$M_a =\{ f\in C[0,1] |\ f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated in $C[0,1]$?
121771
Proof $f(x)\equiv 0$
114812
Let $p(z)=z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+...+a_0$ be a complex polynomial satisfying $|p(z)| \leq 1$ for $|z|\leq 1$, then prove that $p(z)=z^n$
69869
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
69695
$f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$
51687
Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
57669
A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.
144745
Proof of: If $x_0\in \mathbb R^n$ is a point of local minimum of $f$, then $\nabla f(x_0) = 0$.
91388
Prove that $f$ is a polynomial if one of the coefficients in its Taylor expansion is 0
65162
Show that $\dim H^0(\mathbb{P}^n, \mathcal{O}_{\mathbb{P}^n}(m)) = {n + m \choose n}$ if $m \geq 0$, and $0$ otherwise.
130846
Prove or disprove: If $a \in \mathbb{Z}$, $a > 0$, and $p$ is a prime such that $p^4 \mid a^3$, then $p^2 \mid a$.
115299
Elements of $\mathbb{F}_p$ having cube roots in $\mathbb{F}_p$