Example

Let R = Z/2Z and d = X³ + X + 1. Then the residue class a of X in R[X] satisfies

a⁷ = 1.

Indeed, X⁷ - 1 = d · (X⁴ + X² + X + 1) in R[X]. So

a⁷ - 1 = 0 · (a⁴ + a² + a + 1) = 0.