Automated Generation of Anomalous Cancellations
Shalosh B. Ekhad
TL;DR
This paper explores the phenomenon of anomalous digit cancellations in fractions, extending Boas's work by generating numerous examples across different bases using the Extended Euclidean Algorithm.
Contribution
It introduces a novel method employing the Extended Euclidean Algorithm to systematically generate anomalous cancellations across various numerical bases.
Findings
Generated many new examples of anomalous cancellations
Extended Boas's work to multiple bases
Demonstrated the effectiveness of the Euclidean Algorithm in this context
Abstract
If you cancel out the digit 6 from the ratio 16/64, you get the right answer by the wrong method. In 1979 R.P. Boas made an extensive study of such "anomalous cancellations" and generated many examples, in many bases. We continue his pioneering work, and generate many more examples, using the Extended Euclidean Algorithm.
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Taxonomy
TopicsAlgorithms and Data Compression · Advanced Combinatorial Mathematics · Cellular Automata and Applications