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Displaying similar documents to “Representations of integers as sums of primes from a Beatty sequence”

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

Enxun Huang (2023)

Czechoslovak Mathematical Journal

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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.

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

Liqun Hu, Li Yang (2017)

Open Mathematics

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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.

Piatetski-Shapiro sequences

Roger C. Baker, William D. Banks, Jörg Brüdern, Igor E. Shparlinski, Andreas J. Weingartner (2013)

Acta Arithmetica

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Prime Factorization of Sums and Differences of Two Like Powers

Rafał Ziobro (2016)

Formalized Mathematics

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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,...