Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T23:04:48.496Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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