Let(C)(xn-1)denote the set of all distinct irreducible factors of xn-1 in a given finite field.The sufficient and necessary conditions for|(C)(xn-1)|≤3 have been studied in the literature.Using the properties of cyclotomic polynomials in finite fields and other relevant knowledge,we pro-vide the sufficient and necessary conditions for|(C)(xn-1)|=4.
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