# Tagged Questions

Proof that for every $a,b \in \mathbb Z,\ n \in \mathbb N$, that $$a\equiv b \pmod n \iff a \pmod n = b \pmod n.$$ My approach is: $n\mid a$ and $n\mid b$ $a\equiv b \pmod n \iff \exists x,y: ... 1answer 33 views ### How solve$[20]_3^{-1}$? What does this mean,$[20]_3^{-1}$? it's from the topic rings, fields and residue classes. Can you give me a hint how to solve this? 1answer 80 views ### What is zero times zero What is zero zeros? What are no nothings? From a mathematical point of view it would be my thing, but none of us are educated that much in math, so I am curious to hear an expert opinion. 1answer 32 views ### Proving that operations give equal results given equal inputs I was reading about the 9 or 12 basic properties of 'fields' (if that's what they're called) in a book called Spivak's Calculus, 3rd Edition, and got quite befuddled by dealing with as basic stuff as ... 2answers 53 views ### field number theory question If we have${a+b\sqrt{-1}}$for a,b in${Z_p}$, with$p$as an odd prime, with$\sqrt{-1}^2=-1$, how do we show that$a+b\sqrt{-1}$has a multiplicative inverse iff$a-b\sqrt{-1}$has a multiplicative ... 0answers 78 views ### A Gauss sum over a field. Let$K$be a field (not necessarily$\mathbb C$) and let$\zeta=\zeta_n$be a primitive$n$th root of unity in$\bar K$. I would like to know if there is a formula calculating$$\sum_{k=1}^n ... 1answer 101 views ### Why don't I end up with the same splitting field? I've understood that the splitting field of$x^4+2$and the splitting field of$x^4-2$over$\mathbb{Q}$are both the field$\mathbb{Q}(\sqrt[4]{2} , i)$. With degree$8$over$\mathbb{Q}$. This ... 3answers 146 views ### Weird Sub-ring/field? question Let$R=\{\frac{n}{10^{k}} \mid (n,k) \in Z, k>-1\}$which is the sub-ring of the Rational numbers ( assumed true) Consider S a subset of R$S= \{(3/10),(33/100),(333/100),...\}$Show that this ... 2answers 115 views ### Lost on algebra notation I'm in a basic number theory course and, never having taken college algebra, I'm lost on some of the notation. I'm wondering what some of these notations mean: 1:$\mathbb{Q}(i)$... I know that what ... 1answer 642 views ### Cyclotomic polynomial over a finite prime field [duplicate] Possible Duplicate: Irreducible factors of$X^p-1$in$(\mathbb{Z}/q \mathbb{Z})$X$$Let$p$be a prime number. Let$l$be an odd prime number such that$l \neq p$. Let$X^l - 1 \in ...
I'm having trouble with the procedure to find an inverse of a polynomial in a field. For example, take: In $\frac{\mathbb{Z}_3[x]}{m(x)}$, where $m(x) = x^3 + 2x +1$, find the inverse of \$x^2 + ...