Representation of odd integers as the sum of one prime, two squares of primes and powers of 2
Tao Liu (2004)
Acta Arithmetica
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Tao Liu (2004)
Acta Arithmetica
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Janusz Kaja (1982)
Colloquium Mathematicae
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Hongze Li (2001)
Acta Arithmetica
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Hongze Li (2007)
Acta Arithmetica
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L., Hua (1939)
Mathematische Zeitschrift
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M. Z. Garaev (2003)
Acta Arithmetica
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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.
Sakmar, I.A. (2003)
APPS. Applied Sciences
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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.
Nesterenko, Yu.V. (2005)
Journal of Mathematical Sciences (New York)
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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,...
Christian Elsholtz (2008)
Acta Arithmetica
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Alfred Moessner, George Xeroudakes (1954)
Publications de l'Institut Mathématique
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P Erdös (1962)
Acta Arithmetica
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William D. Banks, Ahmet M. Güloğlu, C. Wesley Nevans (2007)
Acta Arithmetica
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M. B. S. Laporta, T. D. Wooley (2001)
Journal de théorie des nombres de Bordeaux
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We prove in this article that almost all large integers have a representation as the sum of a cube, a biquadrate, ..., and a tenth power.