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On $ 4/n=1/x+1/y+1/z$


Author: William A. Webb
Journal: Proc. Amer. Math. Soc. 25 (1970), 578-584
MSC: Primary 10.10
DOI: https://doi.org/10.1090/S0002-9939-1970-0256984-9
MathSciNet review: 0256984
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Abstract: It is shown that the number of positive integers $ n \leqq N$ for which $ 4/n = 1/x + 1/y + 1/z$ is not solvable in positive integers, is less than a constant times $ N/{(\log \;N)^{7/4}}$.

References [Enhancements On Off] (What's this?)

  • [1] Alexander Aigner, Brüche als Summe von Stammbrüchen, J. Reine Angew. Math. 214/215 (1964), 174-179. MR 28 #3969. MR 0160758 (28:3969)
  • [2] L. Bernstein, 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. MR 26 #77. MR 0142508 (26:77)
  • [3] H. Halberstam and K. F. Roth, Sequences, Vol. 1, Clarendon Press, Oxford, 1966. MR 35 #1565. MR 0210679 (35:1565)
  • [4] Karl Prachar, Primzahlverteilung, Springer-Verlag, Berlin and New York, 1957. MR 19, 393. MR 0087685 (19:393b)
  • [5] B. M. Stewart, Theory of numbers, 2nd ed., Macmillan, New York, 1964. MR 37 #6232. MR 0230672 (37:6232)
  • [6] B. M. Stewart and W. A. Webb, Sums of fractions with bounded numerators, Canad. J. Math. 18 (1966), 999-1003. MR 33 #7297. MR 0199148 (33:7297)

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DOI: https://doi.org/10.1090/S0002-9939-1970-0256984-9
Keywords: Diophantine equation, divisors, residue classes, Selberg's sieve
Article copyright: © Copyright 1970 American Mathematical Society

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