Retracted: Digit staircases and a general identity for multiplication by (b-1) - Quilestino-Olario, Raven; Alzola, Maricor Jane R.; Galicia, Maria Bianca C.; Lantaca, JR I.; Pelingon, Kayshe Joy F. (Lietuvos matematikos rinkinys, 2025)
Multiples of nine in base 10 form a staircase pattern: the tens digit increases, the ones digit decreases, and their sum is always nine. We establish a general identity showing that in any base~b, multiplication by (b – 1) produces the same phenomenon. Examples across numeral systems illustrate its link to digital roots and modular arithmetic, while its pedagogical and historical significance highlights how an elementary curiosity fits within number theory and mathematics education.
Keywords: digital root; divisibility by nine; modular arithmetic; number patterns; base-b representation