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

• Mar 6th 2013, 07:52 AM
Panarit
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.
• Mar 6th 2013, 08:15 AM
Plato
Re: I am dealing with a problem and I hope you can help me
Quote:

Originally Posted by Panarit
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 $m\cdot n=(ac-bd)^2+(ad+bc)^2$