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Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 31, No. 2, pp. 207-214 (2015)
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Polynomials with a given cyclic Galois group

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Jiri Cihlar, Jaroslav Fuka and Martin Kuril

J.E. Purkyne University

**Abstract:** For every natural number $n$ such that $2n+1$ is a prime, we present an explicit monic irreducible $n$th degree polynomial with integer coefficients whose Galois group over the field of all rational numbers is isomorphic to the cyclic group $Z_n$. The discriminant of the splitting field of the presented polynomial is equal to $(2n+1)^{n-1}$.

**Keywords:** Galois group of a polynomial, discriminant of a number field.

**Classification (MSC2000):** 12F12; 11R20

**Full text of the article:**

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FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition
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