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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On integers of the form $2^{k} \pm p_{1}^{\alpha _{1}}p_{2}^{\alpha _{2}} \cdots p_{r}^{\alpha _{r}}$


Author: Yong-Gao Chen
Journal: Proc. Amer. Math. Soc. 128 (2000), 1613-1616
MSC (2000): Primary 11A07, 11B25
Published electronically: November 23, 1999
MathSciNet review: 1695159
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Abstract: In this paper we prove that the set of positive odd integers which have no representation of the form $2^{n} \pm p^{\alpha } q^{\beta }$, where $p$, $q$ are distinct odd primes and $n, \alpha ,\beta $ are nonnegative integers, has positive lower asymptotic density in the set of all positive odd integers.


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Additional Information

Yong-Gao Chen
Affiliation: Department of Mathematics, Nanjing Normal University, Nanjing 210097, People’s Republic of China
Email: ygchen@pine.njnu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05482-9
PII: S 0002-9939(99)05482-9
Received by editor(s): July 20, 1998
Published electronically: November 23, 1999
Additional Notes: This research was supported by the Fok Ying Tung Education Foundation and the National Natural Science Foundation of China, Grant No 19701015
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2000 American Mathematical Society