Properties of the Digital Root and its Extension to Rational Numbers -- an Algebraic Approach
arXiv:2110.03746
Abstract
This paper contains an algebraic constructive and self-contained account of the invariance rule of the digital root under division for an arbitrary natural basis representation. Both the cases of repeating and non-repeating fractionals are treated. In the preliminary section some known results such as the uniqueness in the representation of a fraction are discussed for both the finite and infinite bases cases. Simple examples are introduced throughout the text for illustrative purposes.
19 pages