For example, how would I tell that the equation:
x^2 + y^2 + z^2 + 3(x + y + z) + 5 = 0
has no solutions in rational numbers using what I know (rings, groups) from abstract algebra? Or for that matter any other equation? I have hard time understanding why it was so important to take abstract algebra if all the materials don't touch an actual algebra problem on the surface.
x^2 + y^2 + z^2 + 3(x + y + z) + 5 = 0
has no solutions in rational numbers using what I know (rings, groups) from abstract algebra? Or for that matter any other equation? I have hard time understanding why it was so important to take abstract algebra if all the materials don't touch an actual algebra problem on the surface.