We provide a simple algorithm for calculating all generators of power integral bases in pure quintic fields. This procedure involves the usual standard elements like Baker’s method and LLL reduction. The main purpose of this paper is to introduce a new idea to considerably diminish the number of small exponents to be considered after the reduction step. This new idea allows us to test all remaining small exponents within a few minutes, using an appropriate sieve method, which turns out to be surprisingly fast. This idea will be applicable in many similar cases.
István Gaál (2026) studied this question.