query: If $q(x)=x^2+1$, does $q^{\circ 1/2}$ exist?
positive_passages.docid: 144042
positive_passages.text: On the functional square root of $x^2+1$
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: 113230
negative_passages.text: How can we factor $ q^4 + q^2 + 1$
negative_passages.docid: 59442
negative_passages.text: Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
negative_passages.docid: 13248
negative_passages.text: How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
negative_passages.docid: 152509
negative_passages.text: Does there exist a side-rational triangle of area $1$?
negative_passages.docid: 68092
negative_passages.text: Does square difference prove that 1 = 2?
negative_passages.docid: 98255
negative_passages.text: Find $f(x)$ such that $f(f(x)) = x^2 - 2$
negative_passages.docid: 98496
negative_passages.text: Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
negative_passages.docid: 102943
negative_passages.text: $f(x)=1/q$ for $x=p/q$ is integrable
negative_passages.docid: 142845
negative_passages.text: is $y = \sqrt{x^2 + 1}− x$ a injective (one-to-one) function?
negative_passages.docid: 24572
negative_passages.text: Does $n \mid 2^{2^n+1}+1$ imply $n \mid 2^{2^{2^n+1}+1}+1$?
negative_passages.docid: 82321
negative_passages.text: Is $\cos(x) \geq 1 - \frac{x^2}{2}$ for all $x$ in $R$?
negative_passages.docid: 86015
negative_passages.text: $\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
negative_passages.docid: 37158
negative_passages.text: upper limit of $\cos (x^2)-\cos (x+1)^2$ is $2$
negative_passages.docid: 10111
negative_passages.text: Prove or disprove that Q[√2] is a field
negative_passages.docid: 55582
negative_passages.text: How can I show that $\sqrt{1+\sqrt{2+\sqrt{3+\sqrt\ldots}}}$ exists?