De Moivre polynomials of prime degree

Kurt Girstmair

Published 2020-07-28Version 1

Let $p\ge 3$ be an odd natural number. In 1738, Abraham de Moivre introduced a family of polynomials of degree $p$, all of which are solvable. So far, these polynomials were investigated only for $p=5$. We describe the factorization of these polynomials and their Galois groups for arbitrary primes $p\ge 3$. In addition, we express all zeros of such a polynomial as rational functions of three zeros, two of which are "conjugate" in a certain sense.