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On a problem of Erdös, Straus and Schinzel

Published online by Cambridge University Press:  26 February 2010

R. C. Vaughan
R. C. Vaughan
Affiliation:
Department of Pure Mathematics, University of Sheffield.
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Extract

Erdös and Straus have conjectured that for every integer n > 1,

is soluble in positive integers x, y, z. Schinzel has conjectured that for every a > 0 if n > no(a),

is soluble in positive integers x, y, z.

Information

Type
Research Article
Information
Mathematika , Volume 17 , Issue 2 , December 1970, pp. 193 - 198
Copyright
Copyright © University College London 1970

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References

1.Montgomery, H. L., “A note on the large sieve”, J. London Math. Soc., 43 (1968), 93–98.CrossRefGoogle Scholar
2.Davenport, H., Multiplicative number theory (Markham Publishing Co., 1967).Google Scholar
3.Mordell, L. J., Diophantine equations (Academic Press, 1969).Google Scholar
4.Bernstein, L., “Zur Lösung der diophantischen Gleichung m/n = 1/x+1/y+1/z insbesondere im Fall m = 4”, J. reine angew. Math., 211 (1962), 1–10.CrossRefGoogle Scholar
5.Obláth, R., “Sur l'équation diophantienne 4/n = l/x 1+/x 2+l/x 3”, Mathesis, 59 (1949), 308–316.Google Scholar
6.Rosati, L. A., “Sull' equazione diofantea 4/n = l/x 1+/x 2+l/x 3”, Boll. Union Mat. Ital. (3), 9 (1954), 59–63.Google Scholar
7.Yamamoto, K., “On the diophantine equation 4/n = 1/x+1/y+1/z”, Mem. Fac. Sci. Kyushu University Ser. A, 19 (1965), 37–47.Google Scholar
8.Sierpiński, W., “Sur les décompositions de nombres rationnels en fractions primaires”, Mathesis, 65 (1956), 16–32.Google Scholar
9.Palamà, G., “Su di una congettura die Sierpiński relativa alla possibilita in numeri della 5/n = l/x 1 + l/x 2 + l/x 3”, Boll. Union Mat. Ital. (3), 13 (1958), 65–72.Google Scholar
10.Prachar, K., Primzahlverteilung (Springer-Verlag, 1957).Google Scholar
12.Bombieri, E., “On the large sieve”, Mathematika, 12 (1965), 201–225.CrossRefGoogle Scholar