Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# The Properties of the Arithmetic Function as the Consecutive Sum of Digits in Natural Numbers

Version 1 : Received: 5 August 2021 / Approved: 9 August 2021 / Online: 9 August 2021 (07:52:49 CEST)

How to cite: Maleki Chorei, R. The Properties of the Arithmetic Function as the Consecutive Sum of Digits in Natural Numbers. Preprints 2021, 2021080176. https://doi.org/10.20944/preprints202108.0176.v1 Maleki Chorei, R. The Properties of the Arithmetic Function as the Consecutive Sum of Digits in Natural Numbers. Preprints 2021, 2021080176. https://doi.org/10.20944/preprints202108.0176.v1

## Abstract

In this paper defines the consecutive sum of the digits of a natural number, so far as it becomes less than ten, as an arithmetic function called and then introduces some important properties of this function by proving a few theorems in a way that they can be used as a powerful tool in many cases. As an instance, by introducing a test called test, it has been shown that we are able to examine many algebraic equalities in the form of in which and are arithmetic functions and to easily study many of the algebraic and diophantine equations in the domain of whole numbers. The importance of test for algebraic equalities can be considered equivalent to dimensional equation in physics relations and formulas. Additionally, this arithmetic function can also be useful in factorizing the composite odd numbers.

## Keywords

consecutive sum of the digits; algebraic equations; diophantine equations; arithmetic functions

## Subject

Computer Science and Mathematics, Algebra and Number Theory