## Anomalous Cancellation

The simplification of a Fraction which gives a correct answer by canceling'' Digits of and . There are only four such cases for Numerator and Denominators of two Digits in base 10: , , , and (Boas 1979).

The concept of anomalous cancellation can be extended to arbitrary bases. Prime bases have no solutions, but there is a solution corresponding to each Proper Divisor of a Composite . When is Prime, this type of solution is the only one. For base 4, for example, the only solution is . Boas gives a table of solutions for . The number of solutions is Even unless is an Even Square.

 4 1 26 4 6 2 27 6 8 2 28 10 9 2 30 6 10 4 32 4 12 4 34 6 14 2 35 6 15 6 36 21 16 7 38 2 18 4 39 6 20 4 21 10 22 6 24 6

Boas, R. P. Anomalous Cancellation.'' Ch. 6 in Mathematical Plums (Ed. R. Honsberger). Washington, DC: Math. Assoc. Amer., pp. 113-129, 1979.