Behaviour of integers: some peculiar properties

Abstract

The intention of this paper is to highlight certain latent and interesting characteristics of natural numbers and their higher powers vis-a-vis the ultimate sum (single digit sum) of the digits in such integers and their higher powers, their sums and their multiples. The peculiarities owe their characteristics indeed, to the decimal system of integers. And it is the existence of such peculiarities that this paper endeavours to demonstrate. While the author is not aware of any practical use to which the interesting property of integers described in this paper could be put to, it may possibly of some interest to those involved with checks and verification of numerical solutions on computers, apart from of course the number theory buffs.