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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on $4/n=1/x+1/y+1/z$
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by Xun Qian Yang PDF
Proc. Amer. Math. Soc. 85 (1982), 496-498 Request permission

Abstract:

Denoting by $S(N)$ the number of natural numbers $n$ less than $N$ for which \[ \frac {4} {n} = \frac {1} {x} + \frac {1} {y} + \frac {1} {z}\] has no solutions in positive integers, we show that $S(N) \ll N/{\log ^2}N$.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 496-498
  • MSC: Primary 10B20
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0660589-3
  • MathSciNet review: 660589