Chebyshev polynomials and Galois groups of De Moivre polynomials

Let [Formula: see text] be an odd natural number. In 1738, Abraham de Moivre introduced a family of polynomials degree with rational coefficients, all which are solvable. So far, the Galois groups these have been investigated only for prime numbers and under special assumptions. We describe arbitrary in irreducible case, up to few exceptions. addition, we express zeros such polynomial as functions three zeros, two connected certain sense. These results based on reduction irrational irrationals text]. Such was given previous paper author. Here, however, present much simpler approach that is properties Chebyshev polynomials. also give simple proof result Filaseta et al.