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.

• Gauss's Polynomial Theorem
• Gauss's Reciprocity Theorem
• Gauss's Test
• Gauss's Theorem
• Gauss's Theorema Egregium
• Gauss's Transformation
• Gear Graph
• Gegenbauer Function
• Gegenbauer Polynomial
• Gelfond-Schneider Constant
• Gelfond-Schneider Theorem
• Gelfond's Theorem
• Genaille Rods
• Genera
• Generalized Cone
• Generalized Cylinder
• Generalized Fibonacci Number
• Generalized Function
• Generalized Helicoid
• Generalized Helix
• Generalized Hyperbolic Functions
• Generalized Hypergeometric Function
• Generalized Matrix Inverse
• Generalized Mean
• Generalized Remainder Method