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

Chen, Yong Gao; Tang, Min

doi:10.1007/s10114-008-6456-1

Cited by 2 publications

(1 citation statement)

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“…In 2005, Chen [2] proved that there is an arithmetic progression of positive odd numbers such that for each of its terms M, none of the five consecutive odd numbers M, M − 2, M − 4, M − 6 and M − 8 can be expressed in the form 2 n ± p α , where p is a prime and n, α are nonnegative Y.-G. Chen [2] integers. Recently, Chen and Tang [3] presented an explicit arithmetic progression of this type. Chen [1, Corollary 3 with a = 1] proved that there exists an infinite arithmetic progression of positive odd numbers such that for any term k of the sequence and any nonnegative integer n, each of the ten integers…”

Section: Introductionmentioning

confidence: 99%

Eight Consecutive Positive Odd Numbers None of Which Can Be Expressed as a Sum of Two Prime Powers

Chen

2009

Bull. Aust. Math. Soc.

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In this paper we prove the following result: there exists an infinite arithmetic progression of positive odd numbers such that for any term k of the sequence and any nonnegative integer n, each of the 16 integers k−2n, k−2−2n, k−4−2n, k−6−2n, k−8−2n, k−10−2n, k−12−2n, k−14−2n, k2n−1, (k−2)2n−1, (k−4)2n−1, (k−6)2n−1, (k−8)2n−1, (k−10)2n−1, (k−12)2n−1 and (k−14)2n−1 has at least two distinct odd prime factors; in particular, for each term k, none of the eight integers k, k−2, k−4, k−6, k−8, k−10, k−12 or k−14 can be expressed as a sum of two prime powers.

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Section: Introductionmentioning

confidence: 99%