$f$ an entire function and such that $|f(z)| > k|z|^n$ for $|z| > R$.Prove f is a polynomial and find its degree.
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 $n$.
119999
A property of every real polynomial.
141983
Complex polynomial of degree $n$
81063
If $p$ is a polynomial, then either $\,p(z)=z^n\,$ or $\,\max_{|z|=1}|p(z)|>1$.
158561
Let $f (z) $ be an entire function such that $|f (z)|≤K|z|$, $∀z∈\mathbb{C}$, for some $K>0$. If $f (1) =i$, then$f (i) $ is
65901
Solution verification to complex analysis problem, prove $f$ is a polynomial.
26207
If $f$ is a quadratic and $f(x)>0\;\forall x$, and $g= f + f' + f''$, prove $g(x)>0\; \forall x$
101918
Let $f(x)=ax^2+bx+c$ where $a,b,c$ are real numbers. Suppose $f(-1),f(0),f(1) \in [-1,1]$. Prove that $|f(x)|\le \frac{3}{2}$ for all $x \in [-1,1]$.
91388
Prove that $f$ is a polynomial if one of the coefficients in its Taylor expansion is 0
127547
Prove that If $f$ is polynomial function of even degree $n$ with always $f\geq0$ then $f+f'+f''+\cdots+f^{(n)}\geq 0$.
137218
Does there exist a polynomial $f(x)$ with real coefficients such that $f(x)^2$ has fewer nonzero coefficients than $f(x)$?
79359
Show that $f$ is a polynomial if it's the uniform limit of polynomais
97729
Show that a polynomial $f(x)$ over a field $k$ is irreducible if and only if the polynomial $f(x+1)$ is irreducible
148545
Degree of interpolation polynomial
73454
Prove that $f$ has finite number of roots
124460
Show that if $f \in \mathbb{C} \left[x_1, \dots, x_n \right]$ vanishes at every point of $\mathbb{Z}^n$, then $f$ is the zero polynomial.
42265
A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial