If for every $z\in G$ there is $n$ such that $f^{(n)}(z)=0$, then $f$ is a polynomial.
5625
Entire function with vanishing derivatives?
32525
If $f(1)=1$, then is it true that $f(n)=n$ for all $n \in \mathbb{N}\cup\{0\}$.
68071
If $f$ is a nonconstant entire function such that $|f(z)|\geq M|z|^n$ for $|z|\geq R$, then $f$ is a polynomial of degree atleast $n$.
80397
Show that this set of polynomials is ideal in F[x]
100862
Polynomials with rational zeros
129834
Show that there is a unique polynomial of degree at most $2n+1$ such that $q^{[k]}(x_1)=a_k,$ $q^{[k]}(x_2)=b_k$ for $k=0, \dots, n$.
148910
Multivariate polynomials have infinitely many zeroes
148788
Polynomial ring ideal. Show that $(f) \cap R_N = (0) \iff f \notin R_N$
76482
Closure of the set of degree $n$ polynomials with $n$ real roots
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
153107
Does every connected component of $\{z : |P(z)|<1 \}$ contain a zero?
7199
Suppose that $P(x)$ is a polynomial of degree $n$ such that $P(k)=\dfrac{k}{k+1}$ for $k=0,1,\ldots,n$. Find the value of $P(n+1)$
107133
Let f(x) be a polynomial satisfying $\lim_{x \to\infty} \frac{x^4f(x)}{x^8+1}=3,$ $f(2)=5 $ and $f(3)=10$, $f(-1)=2$ and $f(-6)=37$
6484
Polynomials in one variable with infinitely many roots.
76285
Suppose $f$ is entire and $|f(z)| \leq 1/|Re z|^2$ for all $z$. Show that $f $ is identically $0$.
83337
If $A ∈M_n(C)$ is such that $(Ax,x) = 0$ for all $x ∈C^n$, then $A = 0$
33099
If $f$ is an entire function where every power series expansion has at least one 0 term, show it is a polynomial