query: Find all polynomials satisfying $p(x)p(-x)=p(x^2)$
positive_passages.docid: 147047
positive_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: 40426
negative_passages.text: Polynomial degree 3 Equation
negative_passages.docid: 95594
negative_passages.text: Prove that a polynomial is irreducible or the field contains a $p$th root
negative_passages.docid: 47792
negative_passages.text: Integer coefficient polynomial - values as powers of 2
negative_passages.docid: 65661
negative_passages.text: Decomposition of a homogeneous polynomial
negative_passages.docid: 117353
negative_passages.text: Polynomial equation $f(x)f(2x^2)=f(2x^3+x)$
negative_passages.docid: 100862
negative_passages.text: Polynomials with rational zeros
negative_passages.docid: 97028
negative_passages.text: Find all irreducible monic polynomials in $\mathbb{Z}/(2)[x]$ with degree equal or less than 5
negative_passages.docid: 99835
negative_passages.text: Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
negative_passages.docid: 114146
negative_passages.text: Polynomial in $n$ variables
negative_passages.docid: 120627
negative_passages.text: Reducibility of polynomials modulo p
negative_passages.docid: 41689
negative_passages.text: Find all solutions: $x^2 + 2y^2 = z^2$
negative_passages.docid: 135768
negative_passages.text: Find $P(n+1)$ for a polynomial P
negative_passages.docid: 47443
negative_passages.text: Iterated polynomial problem
negative_passages.docid: 156034
negative_passages.text: sufficient condition for a polynomial to have roots in $[0,1]$
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: 118085
negative_passages.text: complex polynomial satisfying inequality