Divisibility rules for integers presented as permutations

Thomas Oliver; Alexei Vernitski

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arXiv · 2502.15559

Divisibility rules for integers presented as permutations

Thomas Oliver·Alexei Vernitski

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Abstract

In this note, we represent integers in a type of factoradic notation. Rather than use the corresponding Lehmer code, we will view integers as permutations. Given a pair of integers n and k, we give a formula for n mod k in terms of the factoradic digits, and use this to deduce various divisibility rules.

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Thomas Oliver, Alexei Vernitski. 2025-02-21. Divisibility rules for integers presented as permutations. https://arxiv.org/abs/2502.15559

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