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Proceedings of the American Mathematical Society

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

 
 

 

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 $N/{(\log \;N)^{7/4}}$.


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Keywords: Diophantine equation, divisors, residue classes, Selberg’s sieve
Article copyright: © Copyright 1970 American Mathematical Society