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An algorithm
for Egyptian fraction representations with restricted
denominators
Greg Martin and Yue Shi |
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Vol. 18 (2025), No. 1, 1–23
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Abstract |
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A unit fraction representation of a rational number is a finite sum of reciprocals of positive integers that equals . Of particular interest is the case when the denominators in the representation are distinct, resulting in an Egyptian fraction representation of . Common algorithms for computing Egyptian fraction representations of a given rational number tend to result in extremely large denominators and cannot be adapted to restrictions on the allowed denominators. We describe an algorithm for finding all unit fraction representations of a given rational number using denominators from a given finite multiset of positive integers. The freely available algorithm, implemented in Scheme and available on GitHub, is particularly well suited to computing dense Egyptian fraction representations, where the allowed denominators have a prescribed maximum. |
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Keywords
Egyptian fractions, unit fractions, number theory,
algorithms, implementation
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Mathematical Subject Classification
Primary: 11D68
Secondary: 11D72
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Milestones
Received: 20 December 2021
Revised: 22 June 2023
Accepted: 12 August 2023
Published: 24 January 2025
Communicated by Filip Saidak
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Authors |
| Greg Martin | |
| Department of Mathematics University of British Columbia Vancouver, BC Canada |
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| Yue Shi | |
| Department of Mathematics Indiana University, Bloomington Bloomington, IN United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
