Number Theory/Complex Numbers
I don't know where to continue with this problem.
It says that if there are two integers which can be expressed as x^2-xy+y^2 for some integers x and y, then their product can also be expressed this way (as X^2-XY+Y^2 for some integers X and Y).
If you let w= e^(2*pi*i/3), then I get |x+y*w| = sqrt(x^2-xy+y^2). Also, (x+wy)(x+w^2y) = x^2-xy+y^2. How would I proceed?
Re: Number Theory/Complex Numbers
nvm, I solved it. I just expanded (x+wy)(x+w^2y) = x^2-xy+y^2 for the two numbers and simplified by combining like terms.