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Math Help - I am dealing with a problem and I hope you can help me

  1. #1
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    I am dealing with a problem and I hope you can help me

    Hi all. I am dealing with a problem and I hope you can help me. I have already proved this:

    Let us suppose that integers m and n can be written as sum of squares of two integers. Prove that m*n can also be written as sum of squares of two integers.


    Now I am trying to prove this:Let us suppose that integers m and n can be written as sum of squares of four integers. Prove that m*n can also be written as sum of squares of four integers.


    Can you help me on this?
    Thank You for reading my post.
    Last edited by Panarit; March 6th 2013 at 08:31 AM.
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  2. #2
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    Re: I am dealing with a problem and I hope you can help me

    Quote Originally Posted by Panarit View Post
    Let us suppose that integers m and n can be written as sum of squares of two integers. Prove that m*n can also be written as sum of squares of two integers.
    Suppose that m=a^2+b^2~\&~n^2=c^2+d^2~.

    Now show that m\cdot n=(ac-bd)^2+(ad+bc)^2
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