Peter Vassilev and Mladen Vassilev-Missana

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 12, 2006, Number 2, Pages 1—7

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## Details

### Authors and affiliations

Peter Vassilev

*CLBME-Bulg. Academy of Sci., Sofia, Bulgaria*

Mladen Vassilev-Missana

*2. V. Hugo Str. 5, ap.3, Sofia-1124, Bulgaria*

### Abstract

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.

### Keywords

- Egyptian fraction
- Unit fraction
- Abundant number
- Pseudoperfect number

### References

- Vassilev, M., Two Theorems Concerning Divisors, Bulletin of Number Theory and Related Topics, Vol. 12, 1988, 10-19
- Stewart,B., Sums of Distinct Divisors, American Journal of Mathematics, Vol. 76,

1954: 779-785 - http://eom.springer.deAa130070.htm
- Dickson, E., History of the theory of numbers, I (Divisibility and primality), 1919

## Related papers

## Cite this paper

APAVassilev, 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.

ChicagoVassilev, Peter, and Mladen Vassilev-Missana. “On Some Solved and Unsolved Problems Related to Egyptian Unit Fractions.” Notes on Number Theory and Discrete Mathematics 12, no. 2 (2006): 1-7.

MLAVassilev, Peter, and Mladen Vassilev-Missana. “On Some Solved and Unsolved Problems Related to Egyptian Unit Fractions.” Notes on Number Theory and Discrete Mathematics 12.2 (2006): 1-7. Print.