In the present work, we obtain a computationally tractable description of the unit group of [Formula: see text] for a class of primes p. This allows us to construct explicit generating sets for the unit group of [Formula: see text], for certain primes p. In addition, we also describe a generating set for the unit group of [Formula: see text], for any positive integer n. Several computational examples are included to illustrate the effectiveness of the method.
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Garcia et al. (2026) studied this question.
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