The Ring $\Z[\sqrt{2}]$ is a Euclidean Domain
Problem 503
Prove that the ring of integers
\[\Z[\sqrt{2}]=\{a+b\sqrt{2} \mid a, b \in \Z\}\]
of the field $\Q(\sqrt{2})$ is a Euclidean Domain.
Add to solve later Tagged: ring of integers
Add to solve later Polynomial $(x-1)(x-2)\cdots (x-n)-1$ is Irreducible Over the Ring of Integers $\Z$
Problem 372
For each positive integer $n$, prove that the polynomial
\[(x-1)(x-2)\cdots (x-n)-1\]
is irreducible over the ring of integers $\Z$.
Add to solve later There is Exactly One Ring Homomorphism From the Ring of Integers to Any Ring
Problem 264
Let $\Z$ be the ring of integers and let $R$ be a ring with unity.
Determine all the ring homomorphisms from $\Z$ to $R$.
Add to solve later 
