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.
- Harmonic Equation
- Harmonic Function
- Harmonic-Geometric Mean
- Harmonic Homology
- Harmonic Logarithm
- Harmonic Map
- Harmonic Mean
- Harmonic Mean Index
- Harmonic Number
- Harmonic Progression
- Harmonic Range
- Harmonic Ratio
- Harmonic Segment
- Harmonic Series
- Harmonic System of Points
- Harmonious Graph
- Harnack's Inequality
- Harnack's Theorems
- Harshad Number
- Hartley Transform
- Hart's Inversor
- Hart's Theorem
- HashLife
- Hasse-Davenport Relation
- Hasse Diagram