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Mathematics of Computation

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Five consecutive positive odd numbers, none of which can be expressed as a sum of two prime powers

Author: Yong-Gao Chen
Journal: Math. Comp. 74 (2005), 1025-1031
MSC (2000): Primary 11A07, 11B25
Published electronically: July 20, 2004
MathSciNet review: 2114663
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Abstract: In this paper, we prove that there is an arithmetic progression of positive odd numbers for each term $M$ of which none of five consecutive odd numbers $M, M-2, M-4, M-6$ and $M-8$ can be expressed in the form $2^n \pm p^\alpha $, where $p$ is a prime and $n, \alpha $ are nonnegative integers.

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Additional Information

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

Keywords: Covering systems, odd numbers, sums of prime powers
Received by editor(s): January 2, 2003
Received by editor(s) in revised form: October 2, 2003
Published electronically: July 20, 2004
Additional Notes: Supported by the National Natural Science Foundation of China, Grant No. 10171046 and the Teaching and Research Award Program for Outstanding Young Teachers in Nanjing Normal University
Article copyright: © Copyright 2004 American Mathematical Society