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On integers of the form $k2^{n}+1$

Author: Yong-Gao Chen
Journal: Proc. Amer. Math. Soc. 129 (2001), 355-361
MSC (2000): Primary 11A07, 11B25
Published electronically: August 28, 2000
MathSciNet review: 1800230
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Abstract: In this paper we show that the set of positive odd integers $k$ such that $ k2^{n} +1$ has at least three distinct prime factors for all positive integers $n$ has positive lower asymptotic density.

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Additional Information

Yong-Gao Chen
Affiliation: Department of Mathematics, Nanjing Normal University, Nanjing 210097, People’s Republic of China

Received by editor(s): April 29, 1999
Published electronically: August 28, 2000
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

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