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Algorithm. Appl."],"published-print":{"date-parts":[[2021,12]]},"abstract":"<jats:p> Let [Formula: see text] be a finite field with [Formula: see text] elements. Let [Formula: see text] be a positive integer with radical [Formula: see text], namely, the product of distinct prime divisors of [Formula: see text]. If the order of [Formula: see text] modulo [Formula: see text] is either 1 or a prime, then the irreducible factorization and a counting formula of irreducible factors of [Formula: see text] over [Formula: see text] were obtained by Mart\u00ednez, Vergara and Oliveira, Explicit factorization of [Formula: see text], Des. Codes Cryptogr. 77(1) (2015) 277\u2013286 and Wu, Yue and Fan, Further factorization of [Formula: see text] over a finite field, Finite Fields Appl. 54 (2018) 197\u2013215. In this paper, we explicitly factorize [Formula: see text] into irreducible factors in [Formula: see text] and calculate the number of the irreducible factors when the order of [Formula: see text] modulo [Formula: see text] is a product of two primes. <\/jats:p>","DOI":"10.1142\/s1793830921500701","type":"journal-article","created":{"date-parts":[[2020,12,14]],"date-time":"2020-12-14T07:15:10Z","timestamp":1607930110000},"source":"Crossref","is-referenced-by-count":6,"title":["Further factorization of xn \u2212 1 over a finite field (II)"],"prefix":"10.1142","volume":"13","author":[{"given":"Yansheng","family":"Wu","sequence":"first","affiliation":[{"name":"School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qin","family":"Yue","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China"},{"name":"State Key Laboratory of Cryptology, P. O. Box 5159, Beijing 100878, P. R. 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