Representation of odd integers as the sum of one prime, two squares of primes and powers of 2
Hongze Li (2007)
Acta Arithmetica
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Hongze Li (2007)
Acta Arithmetica
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Liqun Hu, Li Yang (2011)
Acta Arithmetica
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Hongze Li (2008)
Acta Arithmetica
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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,...
Jianya Liu, Tao Zhan (2001)
Acta Arithmetica
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Hongze Li (2001)
Acta Arithmetica
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Hongze Li (2006)
Acta Arithmetica
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D. I. Tolev (2000)
Acta Arithmetica
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D. I. Tolev (2002)
Acta Arithmetica
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Paul Rowe (2005)
Acta Arithmetica
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L., Hua (1939)
Mathematische Zeitschrift
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Kiss, Elemér (1997)
Mathematica Pannonica
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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.
Lilu Zhao (2014)
Acta Arithmetica
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By developing the method of Wooley on the quadratic Waring-Goldbach problem, we prove that all sufficiently large even integers can be expressed as a sum of four squares of primes and 46 powers of 2.
Kumchev, A., Tolev, D. (2005)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 11D75, 11D85, 11L20, 11N05, 11N35, 11N36, 11P05, 11P32, 11P55. The main purpose of this survey is to introduce the inexperienced reader to additive prime number theory and some related branches of analytic number theory. We state the main problems in the field, sketch their history and the basic machinery used to study them, and try to give a representative sample of the directions of current research.
James G. Huard, Kenneth S. Williams (2003)
Acta Arithmetica
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Guangshi Lü (2007)
Acta Arithmetica
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A. Schinzel (2013)
Bulletin of the Polish Academy of Sciences. Mathematics
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It is proved that all sufficiently large integers satisfying the necessary congruence conditions mod 24 are sums of four squares prime in pairs.
William D. Banks, Ahmet M. Güloğlu, C. Wesley Nevans (2007)
Acta Arithmetica
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Janusz Kaja (1982)
Colloquium Mathematicae
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Roger Clement Crocker (2008)
Colloquium Mathematicae
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It can be shown that the positive integers representable as the sum of two squares and one power of k (k any fixed integer ≥ 2) have positive density, from which it follows that those integers representable as the sum of two squares and (at most) two powers of k also have positive density. The purpose of this paper is to show that there is an infinity of positive integers not representable as the sum of two squares and two (or fewer) powers of k, k again any fixed integer ≥ 2. ...