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On a problem of Erdös, Straus and Schinzel

  • R. C. Vaughan (a1)
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.

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References
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1.Montgomery, H. L., “A note on the large sieve”, J. London Math. Soc., 43 (1968), 9398.
2.Davenport, H., Multiplicative number theory (Markham Publishing Co., 1967).
3.Mordell, L. J., Diophantine equations (Academic Press, 1969).
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), 110.
5.Obláth, R., “Sur l'équation diophantienne 4/n = l/x 1+/x 2+l/x 3”, Mathesis, 59 (1949), 308316.
6.Rosati, L. A., “Sull' equazione diofantea 4/n = l/x 1+/x 2+l/x 3”, Boll. Union Mat. Ital. (3), 9 (1954), 5963.
7.Yamamoto, K., “On the diophantine equation 4/n = 1/x+1/y+1/z”, Mem. Fac. Sci. Kyushu University Ser. A, 19 (1965), 3747.
8.Sierpiński, W., “Sur les décompositions de nombres rationnels en fractions primaires”, Mathesis, 65 (1956), 1632.
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), 6572.
10.Prachar, K., Primzahlverteilung (Springer-Verlag, 1957).
12.Bombieri, E., “On the large sieve”, Mathematika, 12 (1965), 201225.
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Mathematika
  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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