Let m inZ, where m is not a square inZ

Define N:Z[sqrt(m)]--->N

Suppose that : a belongs toZ[sqrt(m)]. If N(a) is a prime inN. Show that a is an atom inZ[sqrt(m)]. Give an example of an m and a inZ[sqrt(m)] such that a is an atom but N(a) is not a prime

Can you give me some hints please?

Thank you