Digital Roots, Rings and Clock Arithmetic

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.