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 [itex]n\inN[/itex], then you can not write u in the from u = a^2 + b^2, where [itex]a,b\inN[/itex]. 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? Please do not post solutions!!!