1. ## Norms and primes

I need an example of an irreducible number in form of a+bsqrt(p) that its norm is not prime.

2. Originally Posted by JCIR
I need an example of an irreducible number in form of a+bsqrt(p) that its norm is not prime.
How do you define the norm of $a+b\sqrt{p}$?

Is it $\sqrt{a^2 + b^2}$?

3. ## norms and prime number

The norm is defined by N(a+bsqrt(p))= /a^2-pb^2/

4. Hello,

Is p prime ?

5. ## norms and primes

p is prime or -1

6. Originally Posted by JCIR
I need an example of an irreducible number in form of a+bsqrt(p) that its norm is not prime.
Consider $\mathbb{Z}[i]$ and then any prime $p\equiv 3(\bmod 4)$ is a Gaussian prime and its norm is $p^2$ - not a prime.

More specifially, $3\in \mathbb{Z}[i]$ and $N(3) = 9$ with $3$ being irreducible.