query: Find all polynomials $p(x)$ such that $p(x^2)={p(x)}^2$
positive_passages.docid: 158148
positive_passages.text: Find all polynomials $P(x)$ such that $P(x^2)=P(x)^2$
negative_passages.docid: 109102
negative_passages.text: Determine all real polynomials with $P(0)=0$ and $P(x^2+1)=(P(x))^2+1$
negative_passages.docid: 147047
negative_passages.text: Does there exist a polynomial $p(x) \in \mathbb C[x]$ such that $p(x) \notin \mathbb R[x]$ and $p(x)p(-x)=p(x^2)$?
negative_passages.docid: 133101
negative_passages.text: Number of solutions of $P(x)=e^{ax}$ if $P$ is a polynomial
negative_passages.docid: 47792
negative_passages.text: Integer coefficient polynomial - values as powers of 2
negative_passages.docid: 132410
negative_passages.text: Difficult Polynomial Question
negative_passages.docid: 139019
negative_passages.text: Polynomial satisfying $f(x) = f'(x) \cdot f''(x)$
negative_passages.docid: 117353
negative_passages.text: Polynomial equation $f(x)f(2x^2)=f(2x^3+x)$
negative_passages.docid: 77403
negative_passages.text: Finding the minimal polynomial of $\sqrt 2 + \sqrt[3] 2$ over $\mathbb Q$.
negative_passages.docid: 152347
negative_passages.text: Proof that a certain entire function is a polynomial
negative_passages.docid: 98255
negative_passages.text: Find $f(x)$ such that $f(f(x)) = x^2 - 2$
negative_passages.docid: 1962
negative_passages.text: Polynomial $P(a)=b,P(b)=c,P(c)=a$
negative_passages.docid: 18053
negative_passages.text: Find all prime $p$ such that $x^2=-1$ has a solution in $\mathbb{Z}/p\mathbb{Z}$
negative_passages.docid: 80502
negative_passages.text: $p(x)$ divided by $x-c$ has remainder $p(c)$? [Polynomial Remainder Theorem]
negative_passages.docid: 154507
negative_passages.text: If all the roots of a polynomial P(z) have negative real parts, prove that all the roots of P'(z) also have negative real parts
negative_passages.docid: 7199
negative_passages.text: 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 $P(n+1)$
negative_passages.docid: 33011
negative_passages.text: Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$