query: Is $π^3$ greater than $3^π$ or conversely?
positive_passages.docid: 22767
positive_passages.text: How to prove $3^\pi>\pi^3$ using algebra or geometry?
negative_passages.docid: 52930
negative_passages.text: Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$
negative_passages.docid: 105405
negative_passages.text: Product of three consecutive positive integers is never a perfect power
negative_passages.docid: 130078
negative_passages.text: How can one prove that $\pi^4 + \pi^5 < e^6$?
negative_passages.docid: 106577
negative_passages.text: If G is not abelian with order $p^3$ then $G'=Z(G)$
negative_passages.docid: 84017
negative_passages.text: Is $\sqrt[3]{2}$ contained in $\mathbb{Q}(\zeta_n)$?
negative_passages.docid: 50663
negative_passages.text: prove or disprove: For a prime number p, there is a positive integer n such that $p+1 $= $n^2$ if and only if $ p = 3.$
negative_passages.docid: 10604
negative_passages.text: Prove $3^n > n^2$ by induction
negative_passages.docid: 71058
negative_passages.text: Is there a value of the function $g$ that is greater than the length of the interval?
negative_passages.docid: 65300
negative_passages.text: Why is $\pi$ irrational?
negative_passages.docid: 126739
negative_passages.text: Is everything greater than None?
negative_passages.docid: 109900
negative_passages.text: Why is $e^{\pi \sqrt{163}}$ almost an integer?
negative_passages.docid: 69874
negative_passages.text: Are there any integer solutions to $a^3=b^2$?
negative_passages.docid: 145891
negative_passages.text: Prove that $n! > \sqrt{n^n}, n \geq 3$
negative_passages.docid: 96805
negative_passages.text: Why is the Absolute Value of $3-π$ equal to $π - 3$
negative_passages.docid: 104498
negative_passages.text: Show that $x^3y^3(x^3+y^3) \leq 2$
negative_passages.docid: 73553
negative_passages.text: How is $a_n=(1+1/n)^n$ monotonically increasing and bounded by $3$?