Post #1815115

@hallasurvivor Pick a, b, c such that \( a^2 + b^2 + c^2 = 1 \), then \( ai + bj + ck \) is a root of -1. Clearly uncountably many solutions. I'm guessing this is the solution the majority of people come up with. Edit. Reinstating my previous claim which was fine actually One property that is no longer true of polynomials is that if they agree on infinitely many places then they are equal. Take \( (x^2 + 1) p(x) \) for a counterexample for two distinct p. You could also observe that, x^4 and x^8 agree infinitely often. I'm not sure what to make of that, although it is basic to how we treat polynomials.