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.