申論題

5. Let n be an integer and n ≥2. Following the steps below to show that xⁿ - x - 1 is irreducible over Q. (You can provide another proof and get the credits.)
For a polynomial

(a) [4%] Let be a monic with f(0) = ±1 such thathave no common root in C. Suppose f(x)=g(x)h(x)for non n-constant.Show that there exists a monic