�ber ein Problem vom Waring-Goldbach'schen Typ

Prachar, K.

doi:10.1007/bf01319081

Cited by 19 publications

(6 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Their methods were consecutively applied to various problems in additive number theory. Among others, Prachar established in 1952, [8] the following result: There exists a constant c > 0 such that all but ≪ x(log x) −c even integers N smaller than x are representable as N = p 2 1 + p 3 2 + p 4 3 + p 4 5 (1.1)…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

A remark on a theorem of the Goldbach-Waring type

Bauer

2004

Studia Scientiarum Mathematicarum Hungarica

View full text Add to dashboard Cite

show abstract

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

A remark on a theorem of the Goldbach-Waring type

Bauer

2004

Studia Scientiarum Mathematicarum Hungarica

View full text Add to dashboard Cite

show abstract

“…Later Prachar [13] improved the above result by proving that almost all positive even integers n can be expressed in the form (1.2) n = p 2 2 + p 3 3 + p 4 4 + p 5 5 .…”

Section: Introductionmentioning

confidence: 89%

An improvement on Waring–Goldbach problem for unlike powers

Liu

2010

Acta Math Hung

View full text Add to dashboard Cite

Let pi be prime numbers. In this paper, it is proved that for any integer k 5, with at most O N 1− 1 3k×2 k−2 +ε exceptions, all positive even integers up to N can be expressed in the form p 2 2 + p 3 3 + p 5 5 + p k k . This improves the result O N log c N for some c > 0 due to Lu and Shan [12], and it is a generalization for a series of results of Ren and Tsang [15], [16] and Bauer [1-4] for the problem in the form p 2 2 + p 3 3 + p 4 4 + p 5 5 . This method can also be used for some other similar forms.

show abstract

“…In 1953, Prachar [4] refined the above result by establishing that almost all positive even integers n can be represented in the form n = p 2 1 + p 3 2 + p 4 3 + p 5 4 , (1.1) where p 1 , p 2 , p 3 and p 4 are prime numbers. Let E(N ) denote the number of positive even integers n up to N , which cannot be expressed in the form (1.1).…”

Section: Introductionmentioning

confidence: 94%

“…Let E(N ) denote the number of positive even integers n up to N , which cannot be expressed in the form (1.1). Prachar [4] proved…”

Section: Introductionmentioning

confidence: 96%