Finite fields

• Find All Irreducible Monic Cubics over the Field with Three Elements
  Over the field with three elements, a monic cubic is irreducible exactly when it has no roots; testing 0, 1, and 2 gives eight polynomials.
• Find All Irreducible Polynomials of Degrees 2 and 3 in F₂[x]
  The irreducible polynomials in F₂[x] of degrees 2 and 3 are x²+x+1, x³+x+1, and x³+x²+1; a root test proves the list.