# Interesting Question

1. Feb 2, 2006

### JasonRox

This isn't homework, but I'll post it anyways because I'd like to know.

It's from Herstein's Abstract Algebra.

Show that if u = 4n + 3, where $n\inN$, then you can not write u in the from u = a^2 + b^2, where $a,b\inN$.

I feel silly for asking this, but I'm curious to know.

The one thing I do, which is obvious is that if a is odd, then b is even because u is odd. But I don't think you need this fact to solve it.

Any directions?

2. Feb 3, 2006

### VietDao29

Okay, I'll give you a hint:
So one of a, and b must be odd, and the other is an even number, right?
So let a = 2k, b = 2x + 1 (k, x are all integers).
Now what's a2 + b2? If you divide a2 + b2 by 4, what's the remainder?
You can take it from here, right? :)

3. Feb 3, 2006

### JasonRox

That's exactly what I did!

I knew something wasn't right when I was looking at it.

I'll give it another shot thanks.