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Math Help - integers

  1. #1
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    integers

    someone to help me with this

    factorise 5550 fully in
    1) the integers
    2) the Gaussian integers?????????
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  2. #2
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    Quote Originally Posted by geo2 View Post
    someone to help me with this

    factorise 5550 fully in
    1) the integers
    2) the Gaussian integers?????????
    I assume you can do 1).

    For 2), you need to know that if p is an integer prime of the form 4k+3 then it is also a Gaussian prime. If it is of the form 4k+1 then it is always possible to express it as a sum of two squares, p=a^2+b^2. Then p factorises in the Gaussian integers as p=(a+ib)(a-ib), and those factors are both Gaussian primes. Finally, 2 factorises in the same way, 2=(1+i)(1-i).

    So for example 11 is a Gaussian prime, but 13 = 3^2+2^2 = (3+2i)(3-2i).
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