>

If d = 1 mod 4, then the integers of the field k(sqrt(d)) are indeed of your form but you must also allow A and B to be both half-integers.

>

> Primes in algebraic number systems:

>

> Consider the extension to the integers,

>

> {A + B * sqrt(d) }, where A, B are variable integers, and d is a

> fixed integer.

See for example Hardy & Wright, Theorem 238.

Mike