# Thread: 3 irreducible in Z[sq.rt.-5]

1. ## 3 irreducible in Z[sq.rt.-5]

How can you show that 3 is irreducible in Z[(-5^(1/2)]?

2. Originally Posted by tomnook
How can you show that 3 is irreducible in Z[(-5^(1/2)]?
You write $3 = (a+bi\sqrt{5})(c+di\sqrt{5})$.
Expand the RHS and compare coefficients.
Now argue that $a=\pm 1, b=0$ or $c=\pm 1, d=0$.
That would $3$ cannot be factored properly and non-trivially.

3. of course! thanks!