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.

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 $\displaystyle m=a^2+b^2~\&~n^2=c^2+d^2~.$

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