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

Authors:	Yong-Gao Chen

Institution:	Department of Mathematics, Nanjing Normal University, Nanjing 210097, Peoples Republic of China

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.

Keywords:	Covering systems odd numbers sums of prime powers

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