IJPAM: Volume 97, No. 1 (2014)
OVER A FINITE FIELD
College of Science
Nanjing University of Aeronautics and Astronautics
Jiangsu, 210016, P.R. CHINA
Abstract. Let be a finite field of odd order . In this paper, the irreducible factorization of over is given in a very explicit form, where are positive integers and are odd prime divisors of . It is shown that all the irreducible factors of over are either binomials or trinomials. In general, denote by the degree of prime in the standard decomposition of the positive integer . Suppose that every prime factor of divides , one has (1) if holds true for every prime number , then every irreducible factor of in is a binomial; (2) if , then every irreducible factor of is either a binomial or a trinomial.
Received: June 26, 2014
AMS Subject Classification: 11T06
Key Words and Phrases: irreducible factorization, binomial, trinomial
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DOI: 10.12732/ijpam.v97i1.7 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 67 - 77
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