Factoring in the Gaussian Integers

[Firepanda]

I need to factorise 70 into primes, how do I go about this?

So far I have 2,5,7 as primes in Z.

So I suppose I need to factorise these in Z?

2 = (1+i)(1-i)

How do I go around doing the other two, is it possible that they're primes in Z?

Edit:

I have a corollary where if p is a prime in Z, then p is a prime in Z if p = 3 mod 4

So 7 stays prime in Z.

Also I have that if the norms of elements in Z are congruent to 1 mod 4 and prime in Z, then the elements in Z are prime, so

5 = (2+1)(2-i) = 1 mod 4

so 70 = 7*(2+1)(2-i)*(1+i)(1-i)

Correct?

Thanks

 

[morphism]

Yes, that's correct.