query: Show that $x^2 + 1$ has an infinite number of roots in Q.
positive_passages.docid: 24837
positive_passages.text: $x^2+1=0$ uncountable many solutions
negative_passages.docid: 42251
negative_passages.text: Limit of non-negative real root of $x^n+x^{n-1}+x-1=0$ as $n \to \infty$
negative_passages.docid: 118916
negative_passages.text: How do I prove that a polynomial F[x] of degree n has at most n roots
negative_passages.docid: 73238
negative_passages.text: Show that $a^{q-1} \equiv 1 \pmod{pq}$
negative_passages.docid: 13909
negative_passages.text: How to find the roots of $x^4 +1$
negative_passages.docid: 61428
negative_passages.text: Show that an algebraically closed field must be infinite.
negative_passages.docid: 150088
negative_passages.text: Prove that $\sqrt {n − 1} +\sqrt {n + 1}$ is irrational for every integer $n ≥ 1$
negative_passages.docid: 45454
negative_passages.text: Pairs of $(p,q)$ such that $p^2 + 1 = 2 q^2$?
negative_passages.docid: 16660
negative_passages.text: Prove that any positive number has an $n$th root
negative_passages.docid: 143321
negative_passages.text: Number of roots of a polynomial over a finite field
negative_passages.docid: 5043
negative_passages.text: Show that $2^n>1+n\sqrt{2^{n-1}}$
negative_passages.docid: 82571
negative_passages.text: Number of solutions of $x^2=1$ in $\mathbb{Z}/n\mathbb{Z}$
negative_passages.docid: 151593
negative_passages.text: Prove that the limit of $\sqrt{n+1}-\sqrt{n}$ is zero
negative_passages.docid: 5410
negative_passages.text: Prove that $a^2 + b^2 \geq 8$ if $ x^4 + ax^3 + 2x^2 + bx + 1 = 0 $ has at least one real root.
negative_passages.docid: 69288
negative_passages.text: Number of real roots of $\sum_{k=0}^{n}\frac{x^{k}}{k!}=0$
negative_passages.docid: 125876
negative_passages.text: Sum and Product of Infinite Radicals
negative_passages.docid: 77076
negative_passages.text: Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$