query: Show that there exists $N \in \mathbb{N}$ such that for every $n \in \mathbb{N}$, one has $a_n = 0$, in other words show $f$ is a polynomial function.
positive_passages.docid: 5625
positive_passages.text: Entire function with vanishing derivatives?
negative_passages.docid: 68071
negative_passages.text: 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 $n$.
negative_passages.docid: 156034
negative_passages.text: sufficient condition for a polynomial to have roots in $[0,1]$
negative_passages.docid: 152347
negative_passages.text: Proof that a certain entire function is a polynomial
negative_passages.docid: 65162
negative_passages.text: 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.
negative_passages.docid: 62239
negative_passages.text: For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
negative_passages.docid: 134342
negative_passages.text: Find a polynomial of degree > 0 in $\mathbb Z_4[X]$ that is a unit.
negative_passages.docid: 66951
negative_passages.text: Proving the existence of a sequence of functions converging to 0 with an added property
negative_passages.docid: 103340
negative_passages.text: Show that this entire function is polynomial.
negative_passages.docid: 80397
negative_passages.text: Show that this set of polynomials is ideal in F[x]
negative_passages.docid: 118873
negative_passages.text: Prove that $f(x)=0$ for all $x\in\mathbb{R}$.
negative_passages.docid: 121304
negative_passages.text: Is the set of polynomials of degree less than or equal to $n$ closed?
negative_passages.docid: 14975
negative_passages.text: Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$
negative_passages.docid: 23125
negative_passages.text: Prove that there is a bijection between the set of all subsets of $X$, $P(X)$, and the set of functions from $X$ to $\{0,1\}$.
negative_passages.docid: 136594
negative_passages.text: Proving the existence of a sequence of polynomials convergent to a continuous function $f$.
negative_passages.docid: 127547
negative_passages.text: Prove that If $f$ is polynomial function of even degree $n$ with always $f\geq0$ then $f+f'+f''+\cdots+f^{(n)}\geq 0$.
negative_passages.docid: 39230
negative_passages.text: Even function has even sequences of polynomials converging uniformly?