Characterising Solutions of Anomalous Cancellation

Anomalous cancellation is a mathematically inaccurate way of reducing fractions where the correct solution is obtained by merely cancelling the common digits in the numerator and denominator. While it appears to be accidentally successful, the property of anomalous cancellation is intricately connected to the number of digits of the denominator as well as the base in which the fraction is represented. Previous work has mostly concerned three-digit solutions or specific properties of the same. This article seeks to obtain general results regarding the structure of numbers that follow the cancellation property (denoted by \(\cal{P}_{\ell;k}^{\ast}\) $${\mathcal{P}}_{\ell ;k}^{\ast }$$ ) and an estimate of the total number of solutions possible in a given base representation. In particular, interesting properties regarding the saturation of the number of solutions in general and pⁿ bases (where p is a prime) have been studied in detail.