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Representation of Even Integers as Sums of Squares of Primes and Powers of 2

โœ Scribed by Jianya Liu; Ming-Chit Liu

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
185 KB
Volume
83
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

As an extension of the Linnik Gallagher results on the ``almost Goldbach'' problem, we prove that every large even integer is a sum of four squares of primes and 8330 powers of 2.

๐Ÿ“œ SIMILAR VOLUMES

Squares of Primes and Powers of 2, II
Squares of Primes and Powers of 2, II
โœ Jianya Liu; Ming-Chit Liu; Tao Zhan ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 143 KB

We prove that the density of integers -2 (mod 24), which can be represented as the sum of two squares of primes and k powers of 4, tends to 1 as k Q . in the sequence k -0 (mod 3). Consequently, there exists a positive integer k 0 such that every large integer -4 (mod 24) is the sum of four squares

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โœ Hisashi Yokota ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 176 KB

Let Nรฐnรž be the set of all integers that can be expressed as a sum of reciprocals of distinct integers 4n: Then we prove that for sufficiently large n; which improves the lower bound given by Croot. # 2002 Elsevier Science (USA)