The parity of the number of irreducible factors of a special polynomial over F_2
Kai He · Scientia Sinica Mathematica · 2010
Using Stickelberger-Swan theorem,we discuss the parity of the number of irreducible factors of the polynomial xl-ef(xf + 1)e + 1 over binary field F2.Our result is compatible with Swan's theorem for square-free binary trinomials,moreover we obtain a similar result for some kinds of binary pentanomial.