Erdős-Straus Conjecture

A conjecture due to Paul Erdős and E. G. Straus that the Diophantine equation

involving Egyptian fractions always can be solved (Obláth 1950, Rosati 1954, Bernstein 1962, Yamamoto 1965, Vaughan 1970, Guy 1994). Swett has established validity of the conjecture for all .

REFERENCES:

Bernstein, L "Zur Lösung der diophantischen Gleichung  insbesondere im Falle ." J. reine angew. Math. 211, 1-10, 1962.

Guy, R. K. "Egyptian Fractions." §D11 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 158-166, 1994.

Obláth, R. "Sur l'equation diophantienne ." Mathesis 59, 308-316, 1950.

Rosati, L. A. "Sull'equazione diofantea ." Boll. Un. Mat. Ital. 9, 59-63, 1954.

Swett, A. "The Erdos-Strauss Conjecture." Rev. 10/28/99. http://math.uindy.edu/swett/esc.htm.

Vaughan, R. C. "On a Problem of Erdős, Straus and Schinzel." Mathematika 17, 193-198, 1970.

Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 29, 1986.

Yamamoto, K. "On the Diophantine Equation ." Mem. Fac. Sci. Kyushu U. Ser. A 19, 37-47, 1965.