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Firepanda
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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
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
Last edited: