On an Embedding Problem

Abstract

The following theorem is proved. Let n be an odd integer; if all primes that occur in the canonical decomposition of the integer $16 + 27n^4$ with odd multiplicities have the form $8m + 1,\;8m + 3$, and $8m + 5$, then the splitting field of the polynomial $f\left( x \right) = x^4 - 2nx - 1$ is embeddable in a nonsplit extension of degree 48. Bibliography: 2 titles.