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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 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
Proc. Amer. Math. Soc. 85 (1982), 496-498
DOI: https://doi.org/10.1090/S0002-9939-1982-0660589-3

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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Bibliographic 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