Mathematics of Computation

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

Author(s): Yong-Gao Chen.
Journal: Math. Comp. 74 (2005), 1025-1031.
MSC (2000): Primary 11A07, 11B25
Posted: July 20, 2004
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Abstract: In this paper, we prove that there is an arithmetic progression of positive odd numbers for each term

of which none of five consecutive odd numbers

and

can be expressed in the form $2^n \pm p^\alpha$ , where

is a prime and $n, \alpha$ are nonnegative integers.

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

DOI: 10.1090/S0025-5718-04-01674-6
PII: S 0025-5718(04)01674-6
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
Posted: 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 of article: Copyright 2004, American Mathematical Society

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