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Digital Roots, Rings and Clock Arithmetic

Published online by Cambridge University Press:  22 September 2016

A. Gardiner*
Affiliation:
Department of Mathematics, University of Birmingham, Birmingham B15 2TT

Extract

The ‘digital root’ of 73219 is 4, since 7 + 3 + 2 +1 + 9 = 22 and 2 + 2 = 4. This idea features in some popular puzzles (and in a recent Gazette note 65.26). Section 1 of this article concerns some basic properties of digital roots, while Section 2 gives a characterisation of functions like the ‘digital root’ function. The former provides interesting exercises in modular arithmetic; the latter in elementary ring theory.

Type
Research Article
Copyright
Copyright © Mathematical Association 1982

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