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On the Diophantine equation

Published online by Cambridge University Press:  01 August 2016

Clotilde Luz Clifton-Everest
Clotilde Luz Clifton-Everest*
Affiliation:
186 Gilbert Road, Cambridge CB4 3PB, e-mail: luzeverest@hotmail.com
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Extract

In this article we discuss two main theorems relating to two different decompositions of the fraction r/n as a sum of three fractions of numerator one. Each decomposition is associated with three positive integers a, b, m such that m is a divisor of an + b. Through this discussion we devise a procedure to find values of a, b and m for a given n.

Type
Articles
Information
The Mathematical Gazette , Volume 91 , Issue 522 , November 2007 , pp. 481 - 492
Copyright
Copyright © The Mathematical Association 2007

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References

1. Erdős, P. and Graham, R.L. Old and new problems and results in combinatorial number theory, Monographies de L’Enseignement Mathématique de Genève 28 (1980) pp. 30–44.Google Scholar
2. Guy, R. K. Unsolved problems in number theory, Springer-Verlag (1981) pp. 87–93.Google Scholar
3. Clifton-Everest, C. Luz Fracçôes Egipcias, Bol. Soc. Port. Mat. 50 (May 2004) pp. 45–78.Google Scholar
4. Clifton-Everest, C. Luz Errata ao meu artigo “Fracçôes Egipcias”, Bol. Soc. Port. Mat. 51 (October 2004) p. 47.Google Scholar
5. Mordell, L. J. Diophantine equations, Academic Press (1969) pp. 287–290.Google Scholar
6. Webb, W. A. Rationals not expressible as a sum of three unit fractions, Elemente der Mathematik 29 (1974) pp. 1–6.Google Scholar
7. Sierpinski, W. Elementary theory of numbers, Monografie Matematyczne 42, Warszawa (1964).Google Scholar
8. Obláth, R. Sur l’équation diophantienne 4/n = 1/x 1 + 1/x 2 + 1/x 3 , Mathesis 59 (1950) pp. 308–316.Google Scholar