Abstract
Let Fq be a finite field of odd order q and m,n be positive integers. In this paper, the irreducible factorization of X2mpn−1 over Fq is given in a very explicit form, where p is an odd prime divisor of q−1. It is shown that all the irreducible factors of X2mpn−1 over Fq are either binomials or trinomials.
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