This paper demonstrates infinitely many permutation-invariant Niven numbers, indicating their unique properties.
This paper introduces permutation-invariant Niven numbers--a novel class of Niven numbers where all digit permutations (with leading zeros automatically ignored) must retain the Niven property. We demonstrate that there exist infinitely many such numbers and that their magnitude is unbounded. Furthermore, we present an exhaustive search method for identifying permutation--invariant Niven numbers.
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Wu et al. (2025) studied this question.
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