In the Euclidean Ring ${\Bbb Z}_3[x]$, what is the remainder of the euclidean division of $x^4+2x^3+x^2+2x+2$ by $x^2+2$?
75120
Polynomial arithmetic uses coefficient ring arithmetic
30752
Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
116453
Is any quotient of a Euclidean domain by a prime ideal a Euclidean domain?
2609
Is there a quick way to find the remainder when this determinant is divided by $5$?
117743
Remainder of the polynomial
14658
Deriving Chinese Remainder Theorem from gcd Bezout identity
53575
Describe $R=\mathbb{Z}[X]/(X^2-3,2X+4)$
154845
Irreducible elements in  $\mathbb{Z}[\sqrt{-2}]$ and is it a Euclidean domain?
68934
Define the polynomial ring $\Bbb Q[c][x]$.Find the $c$ values where $x^2 + x + c + 1$ has a double root.
27278
Let $\alpha \in \overline{\Bbb Q}$ a root of $X^3+X+1\in\Bbb Q[X]$. Calculate the minimum polynomial of $\alpha^{-1}$ en $\alpha -1$.
100720
Negative quotients and their remainders
19112
Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
137610
Finding the field of fractions of a quotient of a polynomial ring.
84017
Is $\sqrt[3]{2}$ contained in $\mathbb{Q}(\zeta_n)$?
5594
Question about the Euclidean ring definition
58803
${n \choose k} \bmod m$ using Chinese remainder theorem?
72640
$(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$