Number theory-product of squares

  1. Number theory--product of squares

    1. The problem statement, all variables and given/known data
    Suppose a and b are two integers, which can each be written as the sum of
    two squares. Prove that ab can be expressed as the sum of two squares.


    2. Relevant equations



    3. The attempt at a solution
    a=c[itex]^{2}[/itex]+d[itex]^{2}[/itex]
    b=x[itex]^{2}[/itex]+y[itex]^{2}[/itex]

    I'm not exactly sure how to approach this proof.
     
  2. jcsd
  3. Re: Number theory--product of squares

    You're on the right track. You've probably tried multiplying them together, and then seeing if you could tease out two squares. The only hint I can give without giving it away (and maybe this gives it away as well) is that you need to add and subtract something in order to get the two squares; they will not be readily apparent.

    Post a little more when you've worked on it further. This won't be too difficult to get, it's probably right under your nose.
     
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