LAUSR

Let ????q be a finite field of odd characteristic containing q elements, and n be a positive integer. An important problem in finite field theory is to factorize xn − 1 into the product of irreducible factors over a finite field. Beyond the realm of theoretical needs, the availability of coefficients of irreducible factors over finite fields is also very important for applications. In this paper, we introduce second order linear recurring sequences in ????q and reformulate the explicit factorization of [Formula: see text] over ????q in such a way that the coefficients of its irreducible factors can be determined from these sequences when d is an odd divisor of q + 1.