Divisibility rules for integers presented as permutations

Published 21 Feb 2025 in math.NT and math.GR | (2502.15559v1)

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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