Exercise 27, § 1

Let A be the quadratic Z-algebra with basis (1, e), where $e^2 = 5$. Show that A is an integral domain ; in A we have $9 = 3 \cdot 3 = (2 + e)(2 - e)$; show that 3, $2 + e$ and $2 - e$ are irreducible elements of A, but do not satisfy the condition in Prop. 14 (DIV) of VI, p. 17.