F_2上一类多项式不可约因子个数的奇偶性

The parity of the number of irreducible factors of a special polynomial over F_2

利用Stickel berger-Swan定理,本文给出了二元域F2上一类特殊形式多项式xl-ef(xf+1)e+1的不可约因子个数的奇偶性,由该结论可得到二元域上非平方三项式的不可约因子个数奇偶性的推论,此推论与Swan给出的关于三项式的定理一致,同时本文还给出了一类五项式在二元域中不可约因子个数奇偶性的类似结论.

Using Stiekelberger-Swan theorem, we discuss the parity of the number of irreducible factors of the polynomial x^l-ef（x^f＋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.