Five consecutive positive odd numbers, none of which can be expressed as a sum of two prime powers
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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.References
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Additional Information
- Yong-Gao Chen
- Affiliation: Department of Mathematics, Nanjing Normal University, Nanjing 210097, Peoples Republic of China
- MR Author ID: 304097
- Email: ygchen@pine.njnu.edu.cn
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Math. Comp. 74 (2005), 1025-1031
- MSC (2000): Primary 11A07, 11B25
- DOI: https://doi.org/10.1090/S0025-5718-04-01674-6
- MathSciNet review: 2114663