Abstract
AbstractOriginally irreducible polynomials were obtained essentially by checking the irreducibility of a randomly chosen polynomial. Recently, irreducible polynomials of a specified form have been produced and a transformation of the variable has been applied to produce a systematic method of deriving irreducible polynomials. In this paper, we consider irreducible polynomials from the viewpoint of cyclotomic polynomials. We define conditions for the existence of irreducible cyclotomic polynomials and show that these polynomials have some specified forms. Additionally, it is shown that an infinite number of irreducible polynomials can be generated which satisfy those conditions.
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