This paper proves finiteness results for perfect powers with two or three digits in canonical number systems, indicating limitations of representations in algebraic number fields.
Extending results of Szalay, Bennett, Bugeaud and Mignotte in this paper, we prove finiteness results concerning perfect powers having two or three digits in their representation in a canonical number system of the equation order of an algebraic number field.
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Bérczes et al. (2025) studied this question.
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