The discussion focuses on identifying all monic irreducible polynomials of degree less than or equal to 3 in the finite fields \(\mathbb{F}_2[x]\) and \(\mathbb{F}_3[x]\). Participants explore the properties of irreducible factors of the polynomial \(x^{p^n} - x\) within the context of \(\mathbb{F}_p[x]\). Key findings include the specific forms of irreducible polynomials in both fields, emphasizing the importance of field characteristics in polynomial factorization.
PREREQUISITESMathematicians, computer scientists, and students studying algebra, particularly those interested in polynomial theory and finite fields.