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In the paper a method named “Continuation of Unity” that is very useful for obtaining infinitely many decompositions of the number 1 with the help of Unit Egyptian fractions starting from given initial decomposition is demonstrated. The important question about decompositions of the number 1 with the help of unit fractions with distinct denominators that belong to a fixed increasing arithmetic progression of natural numbers is discussed. Also some applications related to fractions with odd denominators only are proposed.
- Egyptian fraction
- Unit fraction
- Abundant number
- Pseudoperfect number
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Cite this paper
Vassilev, P., and Vassilev-Missana, M. (2006). On some solved and unsolved problems related to Egyptian unit fractions. Notes on Number Theory and Discrete Mathematics, 12(2), 1-7.