PREreviews of “Self-Healing Numbers: A New Class of Integers with Positional Divisibility Properties”

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Self-Healing Numbers: A New Class of Integers with Positional Divisibility Properties

by Arya Pathak

Posted: September 22, 2025
Server: Preprints.org
DOI: 10.20944/preprints202509.1648.v1

Abstract

We introduce a new class of positive integers called Self-Healing Numbers, defined by a unique positional divisibility property. For each digit position i, the number obtained by removing the digit at position i must be divisible by i. We present complete computational enumerations up to seven digits, establish fundamental structural properties, prove non-hereditary behavior, and analyze the growth of the sequence. Our findings suggest a regular, exponential growth pattern, supporting the conjecture that this sequence is infinite. We also provide a more rigorous mathematical framework by expressing the divisibility conditions as a system of congruences, which allows for deeper theoretical analysis of the number's structure.

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PREreview by Anik Chakraborty

Authored by Anik Chakraborty

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PREreviews of Self-Healing Numbers: A New Class of Integers with Positional Divisibility Properties

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