# Tagged: ring of integers

## 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.

## 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 $\Z$.

## 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 $R$.