EXPLICIT FACTORIZATION OF x 2 a p b r c − 1 OVER A FINITE FIELD
نویسندگان
چکیده
Let Fq be a finite field of odd order q. In this paper, the irreducible factorization of x2 pr − 1 over Fq is given in a very explicit form, where a, b, c are positive integers and p, r are odd prime divisors of q−1. It is shown that all the irreducible factors of x2 pr − 1 over Fq are either binomials or trinomials. In general, denote by vp(m) the degree of prime p in the standard decomposition of the positive integer m. Suppose that every prime factor of m divides q − 1, one has (1) if vp(m) ≤ vp(q−1) holds true for every prime number p|q−1, then every irreducible factor of x − 1 in Fq is a binomial; (2) if q ≡ 3(mod 4), then every irreducible factor of x − 1 is either a binomial or a trinomial. AMS Subject Classification: 11T06
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