Let 𝔽27 denote the finite field of size 27. For each α ∈ 𝔽27, we define
Aα = (1, 1 + α, 1 + α + α2, 1 + α + α2 + α3, ...}.
Then which of the following are true?
1
the number of α ∈ 𝔽27 such that ∣Aα∣ = 26 equals 12
2
0 ∈ Aα if and only if α ≠ 0
3
∣A1∣ = 27
4
\(∩_{α∈𝔽_{27}}A_{\alpha}\) is a singleton set