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 twoDigits 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 asolution 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 tableof 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

References

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

Ogilvy, C. S. and Anderson, J. T. Excursions in Number Theory. New York: Dover, pp. 86-87, 1988.

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