query: Is the product $(p^2+1)/(p^2-1)$ for all $p$ rational? For all $n$?
positive_passages.docid: 153294
positive_passages.text: What is the infinite product of (primes^2+1)/(primes^2-1)?
negative_passages.docid: 132587
negative_passages.text: Prove that the product of coprimes must be congruent to $-1$ or $1 \pmod{m}$
negative_passages.docid: 51679
negative_passages.text: Simplifying the product $\prod\limits_{k=2}^n \left(1-\frac1{k^2}\right)$
negative_passages.docid: 125876
negative_passages.text: Sum and Product of Infinite Radicals
negative_passages.docid: 112390
negative_passages.text: Solutions of $x^2 \equiv 1 \pmod N$
negative_passages.docid: 135768
negative_passages.text: Find $P(n+1)$ for a polynomial P
negative_passages.docid: 142008
negative_passages.text: Find all natural numbers $n$ such that ${(n+1)}^{1/2}-{(n-1)}^{1/2}$ is rational
negative_passages.docid: 100361
negative_passages.text: Show that ord$_{p}2 = 2^{n + 1}$.
negative_passages.docid: 20034
negative_passages.text: Does $a^2+b^2=1$ have infinitely many solutions for $a,b\in\mathbb{Q}$?
negative_passages.docid: 44600
negative_passages.text: How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
negative_passages.docid: 154945
negative_passages.text: $|px^2+qx+r|\le1$ for all $x$ in $[-1; 1]$, show that $|rx^2+qx+p|\le2$ for all $x$ in $[-1; 1]$
negative_passages.docid: 130499
negative_passages.text: How can $p^{q+1}+q^{p+1}$ be a perfect square?
negative_passages.docid: 19254
negative_passages.text: How many rationals of the form $\large \frac{2^n+1}{n^2}$ are integers?
negative_passages.docid: 71482
negative_passages.text: Solve $p_4(x) = x^4 −(2m + 4)x^2 + (m−2)^2 $such that $p_4$ is a product of two non-constant integer-coeficient polynomials
negative_passages.docid: 82571
negative_passages.text: Number of solutions of $x^2=1$ in $\mathbb{Z}/n\mathbb{Z}$
negative_passages.docid: 151520
negative_passages.text: About the parity of the product $(a_1-1)(a_2-2)\cdots(a_n-n)$
negative_passages.docid: 13904
negative_passages.text: $p = x^2 + xy + y^2$ if and only if $p \equiv 1 \text{ mod }3$?