query: Prove that if a polynomial f is constant for infinitely many arguments then it is constant.
positive_passages.docid: 27540
positive_passages.text: A polynomial can not have infinite number of constant values
negative_passages.docid: 11158
negative_passages.text: Proof that a continuous function with $f(x) = f(x^2)$ is constant.
negative_passages.docid: 71799
negative_passages.text: A complex polynomial with partial derivatives equal to zero is constant.
negative_passages.docid: 55119
negative_passages.text: Proof that the coefficients of a polynomial are real
negative_passages.docid: 5416
negative_passages.text: How does one prove if a multivariate function is constant?
negative_passages.docid: 148451
negative_passages.text: Polynomial inequality proof
negative_passages.docid: 156034
negative_passages.text: sufficient condition for a polynomial to have roots in $[0,1]$
negative_passages.docid: 107133
negative_passages.text: 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 $f(-6)=37$
negative_passages.docid: 2527
negative_passages.text: Entire function bounded by a polynomial is a polynomial
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: 69804
negative_passages.text: Prove that if $f$ is entire and $\vert f(z^2) \vert \leq 2 \vert f(z) \vert$, then $f$ is constant
negative_passages.docid: 91352
negative_passages.text: If $\Re(f)$ is bounded then f is constant.
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: 136594
negative_passages.text: Proving the existence of a sequence of polynomials convergent to a continuous function $f$.
negative_passages.docid: 145919
negative_passages.text: If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant.
negative_passages.docid: 27772
negative_passages.text: Let $f$ be an analytic function such that $\operatorname{Im}(f(z))=\operatorname{Re}(f(z))^2$. Prove that $f$ is constant.
negative_passages.docid: 137043
negative_passages.text: To show that function is constant