Self-Reciprocal Irreducible Pentanomials Over F_2

摘要

Joseph Yucas and Gary Mullen conjectured that there is no self-reciprocal irreducible pentanomial of degree n over F_2 if n is divisible by 6. In this note we prove this conjecture for the case n ≡ 0 (mod 12), and disprove the conjecture for the case n ≡ 6 (mod 12).