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Showing 1 to 2 of 2 for “"Egyptian Fraction"”.
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On the Number of Representations of One as the Sum of Unit Fractions
The Egyptian Fractions of One problem (EFO), asks the following question: Given a positive integer n, how many ways can 1 be expressed as the sum of n non-increasing unit fractions? In this paper, we verify a result concerning the EFO problem for n=8, and show the computational complexity of the …
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Topics in Probabilistic Combinatorics
… Finally, in Chapter 9, we are interested in Egyptian fractions. For a prime number $p$, we let $A_3(p)= | \{ m \in \mathbb{N}: \exists m_1,m_2,m_3 \in \mathbb{N}, \frac{m}{p}=\frac{1}{m_1}+\frac{1}{m_2}+\frac{1}{m_3} \} |$ be the number of fractions with denominator $p$ that can be written as …