Polynomials with a given cyclic Galois group

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

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