#77 — November 1, 2025 by Evan Chen

Someone told me that $$\left( \frac{1+\sqrt5}{2} \right)^3 = 2 + \sqrt 5$$ and I feel kind of spooked. Doesn't feel right that the denominator disappears.

Well, $\mathbb Z[\sqrt 5]$ isn't integrally closed. Maybe that's a good way to drive that point home.