All the solutions of the equation \(\sum ^{11}_{i=1} \frac{1}{x_i}= 1\) in distinct integers of the form \(x_i \in 3^{\alpha} 5^{\beta} 7^{\gamma}\)

DOI10.1016/j.disc.2007.08.049zbMath1169.11016OpenAlexW2578859391MaRDI QIDQ941363

Nechemia Burshtein

Publication date: 4 September 2008

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2007.08.049

zbMATH Keywords

representation of integerssum of Egyptian fractionsexplicit solution of a special Diophantine equation in integers of the form \(3^\alpha 5^\beta 7^\gamma\)

Mathematics Subject Classification ID

Rational numbers as sums of fractions (11D68)

Related Items (2)

The equation \(\sum ^9_{i=1} \frac {1}{x_i} = 1\) in distinct odd integers has only the five known solutions ⋮ On arithmetical structures on complete graphs

Cites Work

• The equation \(\sum ^9_{i=1} \frac {1}{x_i} = 1\) in distinct odd integers has only the five known solutions
• Unsolved problems in number theory
• On distinct unit fractions whose sum equals 1
• Unnamed Item

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