query: Rational algebraic numbers
positive_passages.docid: 148310
positive_passages.text: Showing rational numbers are algebraic
negative_passages.docid: 103744
negative_passages.text: Minimal $ab$ for Rational Number $a/b$ in an Interval
negative_passages.docid: 63390
negative_passages.text: Infinite algebraic extensions of $\mathbb{Q}$
negative_passages.docid: 41486
negative_passages.text: If $x^n + a_{n-1}x^{n-1} + ... + a_0 = 0$ has a rational root, then such root is an integer
negative_passages.docid: 115834
negative_passages.text: Cubic polynomial with three (distinct) irrational roots
negative_passages.docid: 87994
negative_passages.text: Find rational points on $x^2 + y^2 = 3$ and on $x^2 + y^2 = 17$
negative_passages.docid: 89496
negative_passages.text: $a$ algebraic number, $\exists$ integer $n>0$ such that $na$ algebraic integer
negative_passages.docid: 147459
negative_passages.text: Find a non-constructible algebraic number of degree $4$ over $\Bbb Q$
negative_passages.docid: 122487
negative_passages.text: Degree of Rational Function
negative_passages.docid: 5287
negative_passages.text: Representing every positive rational number in the form of $(a^n+b^n)/(c^n+d^n)$
negative_passages.docid: 72670
negative_passages.text: Find three distinct triples (a, b, c) consisting of rational numbers that satisfy $a^2+b^2+c^2 =1$ and $a+b+c= \pm 1$.
negative_passages.docid: 55302
negative_passages.text: Rational values of trigonometric functions
negative_passages.docid: 32516
negative_passages.text: show that rational numbers with the multipiciation are not abelian finitely generated group
negative_passages.docid: 107089
negative_passages.text: finding rational roots of polynomials
negative_passages.docid: 114442
negative_passages.text: Completion of rational numbers via Cauchy sequences
negative_passages.docid: 46561
negative_passages.text: How can I prove that all rational numbers are either terminating decimal or repeating decimal numerals?
negative_passages.docid: 142008
negative_passages.text: Find all natural numbers $n$ such that ${(n+1)}^{1/2}-{(n-1)}^{1/2}$ is rational