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Displaying similar documents to “The number of powers of 2 in a representation of large even integers by sums of such powers and of two primes (II)”

On pairs of equations in unlike powers of primes and powers of 2

Liqun Hu, Li Yang (2017)

Open Mathematics

Similarity:

In this paper, we obtained that when k = 455, every pair of large even integers satisfying some necessary conditions can be represented in the form of a pair of unlike powers of primes and k powers of 2.

On pairs of Goldbach-Linnik equations with unequal powers of primes

Enxun Huang (2023)

Czechoslovak Mathematical Journal

Similarity:

It is proved that every pair of sufficiently large odd integers can be represented by a pair of equations, each containing two squares of primes, two cubes of primes, two fourth powers of primes and 105 powers of 2.

Prime Factorization of Sums and Differences of Two Like Powers

Rafał Ziobro (2016)

Formalized Mathematics

Similarity:

Representation of a non zero integer as a signed product of primes is unique similarly to its representations in various types of positional notations [4], [3]. The study focuses on counting the prime factors of integers in the form of sums or differences of two equal powers (thus being represented by 1 and a series of zeroes in respective digital bases). Although the introduced theorems are not particularly important, they provide a couple of shortcuts useful for integer factorization,...

Primes in tuples IV: Density of small gaps between consecutive primes

Daniel Alan Goldston, János Pintz, Cem Yalçın Yıldırım (2013)

Acta Arithmetica

Similarity:

We prove that given any small but fixed η > 0, a positive proportion of all gaps between consecutive primes are smaller than η times the average gap. We show some unconditional and conditional quantitative results in this vein. In the results the dependence on η is given explicitly, providing a new quantitative way, in addition to that of the first paper in this series, of measuring the effect of the knowledge on the level of distribution of primes.