I need to factorise 70 into primes, how do I go about this?(adsbygoogle = window.adsbygoogle || []).push({});

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 Zif p = 3 mod 4

So 7 stays prime in Z.

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

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

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

Correct?

Thanks

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# Homework Help: Factoring in the Gaussian Integers

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