1. ## Sum of squares

Any hints on this?

It appears 2x( 32+52) can be expressed as 82+ 22

I am thinking is it the case that 2x(a2 +b2) can be expressed as a sum of two integer squares for any integers a and b?

I can't see a way of manipulating the expression to do anything?

2. ## Re: Sum of squares

Ok, I think i have worked this out..

Is it case of 2(a^2+ b^2) = (a+b)^2 + (a-b)^2 ???

3. ## Re: Sum of squares

Originally Posted by rodders
Ok, I think i have worked this out..
Is it case of 2(a^2+ b^2) = (a+b)^2 + (a-b)^2 ???
Why doubt your self? Do you understand why?
\begin{align*}(a+b)^2+(a-b)^2&=(a^2+2ab+b^2)+(a^2-2ab+b^2) \\&=2a^2+2b^2\\&=2(a^2+b^2) \end{align*}

Pick any two numbers, say $7~\&~15$. Now $7^2=49~\&~15^2=225$ also $(7+15)^2=484~\&~(1-15)^2=64$
Does it work?

4. ## Re: Sum of squares

Originally Posted by Plato

... also $(7+15)^2=484~\&~(1-15)^2=64$
Does it work?
$(7 - 15)^2 = 64$