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 | References | Similar Articles | Additional Information

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 , where is a prime and 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

Email:
ygchen@pine.njnu.edu.cn

DOI:
https://doi.org/10.1090/S0025-5718-04-01674-6

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

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