query: What's $-\frac{1}{27}$ in the p-adic ring $\Bbb Z_2$?
positive_passages.docid: 149381
positive_passages.text: Relating the base-p periodic expansion of a rational to its p-adic representation
negative_passages.docid: 34668
negative_passages.text: Find all rings $R$ satisfying $\mathbb Z \subset R \subset \mathbb Z[\frac {1}{2}]$
negative_passages.docid: 76840
negative_passages.text: How to show that the modulus of $\frac{z-w}{1-\bar{z}w}$ is always $1$?
negative_passages.docid: 9794
negative_passages.text: Quotient ring of Gaussian integers $\mathbb{Z}[i]/(a+bi)$ when $a$ and $b$ are NOT coprime
negative_passages.docid: 86807
negative_passages.text: The units of $\mathbb Z[\sqrt{2}]$
negative_passages.docid: 124864
negative_passages.text: A not free $\mathbb{Z}$-module
negative_passages.docid: 156834
negative_passages.text: Why are there $736$ matrices $M\in \mathcal M_2(\mathbb{Z}_{26})$ for which it holds that $M=M^{-1}$?
negative_passages.docid: 77470
negative_passages.text: Find modulus of $\frac{|z_1-z_2|}{|1-(z_1)(\overline{z_2})|}$
negative_passages.docid: 19884
negative_passages.text: The units of $\mathbb Z_4[x]$
negative_passages.docid: 7109
negative_passages.text: 2-adic valuation of odd harmonic sums
negative_passages.docid: 124230
negative_passages.text: What is $\operatorname{Hom}_\mathbb{Z}(\mathbb{Q}/\mathbb{Z},\mathbb{Q}/\mathbb{Z})$?
negative_passages.docid: 141331
negative_passages.text: What is a $p$-adic group
negative_passages.docid: 67705
negative_passages.text: Square roots in the $p$-adics
negative_passages.docid: 78118
negative_passages.text: Algebraically, why is $\mathbb{Z}[i]/(i + 1)$ isomorphic to $\mathbb{Z}_{2}$?
negative_passages.docid: 121255
negative_passages.text: Ideals of the ring of rational numbers with odd denominators
negative_passages.docid: 153664
negative_passages.text: When is $\Bbb{Z[\zeta_n]}$ a PID?
negative_passages.docid: 39492
negative_passages.text: Finding $z\in \mathbb C$ with $\sin z = 2$?