Cyclotomic Field

The smallest field containing $m\in \Bbb{Z}\geq 1$ with $\zeta$ a Prime Root of Unity is denoted $\Bbb{R}_m(\zeta)$.

$$x^p+y^p=\prod_{k=1}^p (x+\zeta^k y).$$

Specific cases are

$$\Bbb{R}_3 = \Bbb{Q}(\sqrt{-3}\,)$$

$$\Bbb{R}_4 = \Bbb{Q}(\sqrt{-1}\,)$$

$$\Bbb{R}_6 = \Bbb{Q}(\sqrt{-3}\,),$$

where $\Bbb{Q}$ denotes a Quadratic Field.